House pricing: simulation activity in R

Spatial Modeling of Housing Prices

Housing Price Data in Hennepin and Ramsey county, Minneapolis, Minnesota

The Hennepin and Ramsey housing prices are gathered aggregate summaries of the people who live in Hennepin and Ramsey county, summarized for each census tract based on data from 2015-2019 American Community Service run by the U.S. Census Bureau. A census tract is a statistical subdivision of a county that aims to have roughly 4,000 inhabitants and they are intended to be fairly homogeneous with respect to demographic and economic conditions. #need revision

load('SpatialData.RData')
ggplot(mn_data, aes(x=HouseValueE))+
  geom_density()

This dataset contains housing data of 464 Hennepin and Ramsey census tracts including median prices of housing in USD (HouseValueE), median household income in the past 12 months (in 2019 inflation) (IncomeE), and average household size of occupied houses (HouseholdSizeE). We create the variable called vble with the logarithm of the median prices to put it in the same scale, and map the log price using mapview (Figure 1). The map suggests that the housing prices are greater in the southwest, and prices are related to those in neighboring areas. Noted that the empty area is the University of Minnesota area, since there is no houses listed.

Figure 1 Logarithm of housing prices in Hennipin & Ramsey county, MN per census tract from the spData package

mn_data$vble <- log(mn_data$HouseValueE)
mapview(mn_data, zcol = "vble")

We will model the logarithm of the median prices using as covariates the average Median household income in the past 12 months (IncomeE) and the average household size (HouseholdSizeE). Figure 2 shows the relationships between pairs of variables visualized using the ggpairs() function of the GGally package (Schloerke et al. 2021). We observe a negative relationship between the logarithm of housing price and crime, and a positive relationship between the logarithm of housing price and the average number of rooms.

Figure 2 Relationship betwen the outcome variable logarithm of housing price (vble), and the average Median household income in the past 12 months (IncomeE) and the average household size (HouseholdSizeE)

# Find relationship of crime rate and number of rooms with log(house price)
ggpairs(data = mn_data, columns = c("vble", "HouseholdSizeE", "IncomeE"))

Model

Let \(Y_i\) be the logarithm of housing price of area \(i\), \(i = 1 , \dots, n\). We fit a BYM model that considers \(Y_i\) as the response variable, and household income and household size as covariates: \[ Y \sim N(\mu_i,\sigma^2), i = 1, \dots, n \\ \mu_i=\beta_0+\beta_1 \times Income+\beta_2 \times HouseholdSize + u_i+v_i \] where, (Question? does this mean that each household has a seperate intercept) - \(\beta_0\): the global intercept, which every household will have the same intercept. - \(\beta_1\), \(\beta_2\): represent respectively, the coefficients of the covariates household income and household size. - \(\mu_i\): a spatially structured effect modeled with a CAR structure,\(\mu_i| u_{-i} \sim N(\mu_{\delta_i}, \frac{\sigma^2_u}{n_{\delta_i}})\). - \(v_i\): an unstructured effect modeled as \(v_i \sim N(\theta, \sigma^2_v)\).

Neighborhood Matrix

We decided to use Queen neighborhood structure, which …

Figure 3 Neighborhood Network Structure

In the model, the spatial random effect \(u_i\) needs to be specified using a neighborhood structure. As we mentioned in the spatial model section, there are 3 commmon neighborhood structure: Queen, Rook, and Bishop. Here, we assume two areas are neighbors if they share a common edge or a common vertex. We create a neighborhood structure using functions of the spdep package (Bivand 2022).

First, we use the poly2nb() function to generate a spatial weights matrix (nb) based on the data (mn_data) and using queen contiguity to define neighborhood relationships between polygons. Each element of the list nb represents one area and contains the indices of its neighbors. For example, nb[[1]] contains indices of neighboring polygons in area 1.

# Neighborhood
nb <- poly2nb(mn_data, queen = TRUE)
head(nb, 3)
[[1]]
[1]  50  64 122 177 241 423 457

[[2]]
[1] 145 180 276 339 365

[[3]]
[1] 128 266 337 385 463

Figure 3 shows a map with the neighbors obtained. This plot is obtained by first plotting the map of Ramsey and Hennipin, and then overlapping the queen neighborhood structure with the plot.nb() function passing the neighbor list and the coordinates of the map.

plot(st_geometry(mn_data), border = "black")
plot.nb(nb, st_geometry(mn_data), add = TRUE)

To construct the neighborhood matrix that can be used in the INLA function, we use the nb2INLA() function to convert the nb list into a file called map.adj. This step will make sure that we have the representation of the neighborhood matrix as required by R-INLA. The map.adj file is saved in the working directory which can be obtained with getwd(). Then, we read the map.adj file using the inla.read.graph() function of R-INLA, and store it in the object g which we later use to specify the spatial model using R-INLA.

nb2INLA("map.adj", nb)
g <- inla.read.graph(filename = "map.adj")

mn_data$re_u <- 1:nrow(mn_data)
mn_data$re_v <- 1:nrow(mn_data)

prior <- list(
  prec = list(
    prior = "pc.prec",
    param = c(0.5 / 0.31, 0.01)),
  phi = list(
    prior = "pc",
    param = c(0.5, 2 / 3))
  )

# Specify BYM model
formula <- vble ~ 
  f(re_u, model = "besag", graph = g, scale.model = TRUE) +
  f(re_v, model = "iid")

formula <- vble ~ f(re_u, model = "bym2", graph = g, hyper = prior)

res <- inla(formula, family = "gaussian", data = mn_data,
            control.predictor = list(compute = TRUE),
            control.compute = list(return.marginals.predictor = TRUE))

res$summary.fixed
                mean           sd 0.025quant 0.5quant 0.975quant
(Intercept) 12.70831 0.0004635248   12.70734 12.70831   12.70928
                mode          kld
(Intercept) 12.70831 0.0006254889
summary(res$summary.fitted.values)
      mean             sd             0.025quant       0.5quant    
 Min.   :11.89   Min.   :0.009514   Min.   :11.87   Min.   :11.89  
 1st Qu.:12.47   1st Qu.:0.009533   1st Qu.:12.45   1st Qu.:12.47  
 Median :12.68   Median :0.009537   Median :12.66   Median :12.68  
 Mean   :12.71   Mean   :0.009543   Mean   :12.69   Mean   :12.71  
 3rd Qu.:12.92   3rd Qu.:0.009543   3rd Qu.:12.90   3rd Qu.:12.92  
 Max.   :13.94   Max.   :0.009846   Max.   :13.92   Max.   :13.94  
   0.975quant         mode      
 Min.   :11.91   Min.   :11.89  
 1st Qu.:12.49   1st Qu.:12.47  
 Median :12.70   Median :12.68  
 Mean   :12.73   Mean   :12.71  
 3rd Qu.:12.94   3rd Qu.:12.92  
 Max.   :13.96   Max.   :13.94  
# Posterior mean and 95% CI
mn_data$PM <- res$summary.fitted.values[, "mean"]
mn_data$LL <- res$summary.fitted.values[, "0.025quant"]
mn_data$UL <- res$summary.fitted.values[, "0.975quant"]
mapsf <- st_as_sf(mn_data)

gRR <- ggplot(mn_data) + geom_sf(aes(fill = PM)) +
  scale_fill_gradient2( midpoint = 12.5,low = "blue", high = "red") +
  theme_bw()
gLL <- ggplot(mn_data) + geom_sf(aes(fill = LL)) +
  scale_fill_gradient2(midpoint = 12.5, low = "blue", high = "red") +
  theme_bw()
gUL <- ggplot(mn_data) + geom_sf(aes(fill = LL)) +
  scale_fill_gradient2(midpoint = 12.5, low = "blue", high = "red") +
  theme_bw()

library(cowplot)
plot_grid(gRR, gLL, gUL, ncol = 1)

# common legend
at <- seq(min(c(mn_data$PM, mn_data$LL, mn_data$UL)),
          max(c(mn_data$PM, mn_data$LL, mn_data$UL)),
          length.out = 8)

# popup table
popuptable <- leafpop::popupTable(dplyr::mutate_if(mn_data,
                                  is.numeric, round, digits = 2),
zcol = c("NAME", "vble", "HouseholdSizeE", "IncomeE", "PM", "LL", "UL"),
row.numbers = FALSE, feature.id = FALSE)

m1 <- mapview(mn_data, zcol = "PM", map.types = "CartoDB.Positron",
              at = at, popup = popuptable)
m2 <- mapview(mn_data, zcol = "LL", map.types = "CartoDB.Positron",
              at = at, popup = popuptable)
m3 <- mapview(mn_data, zcol = "UL", map.types = "CartoDB.Positron",
              at = at, popup = popuptable)

m <- leafsync::sync(m1, m2, m3, ncol = 3)
m
# Transformation of the marginal of
# the first area with inla.tmarginal()
# inla.tmarginal(function(x) exp(x),
#                res$marginals.fitted.values[[1]])

# Transformation marginals with inla.tmarginal()
marginals <- lapply(res$marginals.fitted.values,
FUN = function(marg){inla.tmarginal(function(x) exp(x), marg)})

# Obtain summaries of the marginals with inla.zmarginal()
marginals_summaries <- lapply(marginals,
FUN = function(marg){inla.zmarginal(marg)})
Mean            306296 
Stdev           2900.27 
Quantile  0.025 300290 
Quantile  0.25  304767 
Quantile  0.5   306245 
Quantile  0.75  307748 
Quantile  0.975 312635 
Mean            350380 
Stdev           3315.76 
Quantile  0.025 343317 
Quantile  0.25  348663 
Quantile  0.5   350368 
Quantile  0.75  352074 
Quantile  0.975 357434 
Mean            219331 
Stdev           2076.56 
Quantile  0.025 214974 
Quantile  0.25  218246 
Quantile  0.5   219308 
Quantile  0.75  220381 
Quantile  0.975 223814 
Mean            260598 
Stdev           2467.64 
Quantile  0.025 255511 
Quantile  0.25  259293 
Quantile  0.5   260548 
Quantile  0.75  261829 
Quantile  0.975 266015 
Mean            193449 
Stdev           1831.12 
Quantile  0.025 189639 
Quantile  0.25  192486 
Quantile  0.5   193421 
Quantile  0.75  194369 
Quantile  0.975 197434 
Mean            260214 
Stdev           2462.97 
Quantile  0.025 255011 
Quantile  0.25  258932 
Quantile  0.5   260195 
Quantile  0.75  261465 
Quantile  0.975 265497 
Mean            529419 
Stdev           5004.63 
Quantile  0.025 518685 
Quantile  0.25  526839 
Quantile  0.5   529420 
Quantile  0.75  531991 
Quantile  0.975 539990 
Mean            192829 
Stdev           1825.09 
Quantile  0.025 189003 
Quantile  0.25  191875 
Quantile  0.5   192809 
Quantile  0.75  193752 
Quantile  0.975 196773 
Mean            196004 
Stdev           1859.56 
Quantile  0.025 192216 
Quantile  0.25  195014 
Quantile  0.5   195956 
Quantile  0.75  196923 
Quantile  0.975 200131 
Mean            273620 
Stdev           2590.9 
Quantile  0.025 268155 
Quantile  0.25  272270 
Quantile  0.5   273598 
Quantile  0.75  274934 
Quantile  0.975 279185 
Mean            271463 
Stdev           2570.22 
Quantile  0.025 266107 
Quantile  0.25  270114 
Quantile  0.5   271426 
Quantile  0.75  272756 
Quantile  0.975 277049 
Mean            474637 
Stdev           4491.5 
Quantile  0.025 465017 
Quantile  0.25  472321 
Quantile  0.5   474635 
Quantile  0.75  476942 
Quantile  0.975 484141 
Mean            616710 
Stdev           5835.16 
Quantile  0.025 604049 
Quantile  0.25  613727 
Quantile  0.5   616746 
Quantile  0.75  619732 
Quantile  0.975 628895 
Mean            339066 
Stdev           3209.68 
Quantile  0.025 332357 
Quantile  0.25  337383 
Quantile  0.5   339024 
Quantile  0.75  340684 
Quantile  0.975 346021 
Mean            308379 
Stdev           2916.22 
Quantile  0.025 302164 
Quantile  0.25  306870 
Quantile  0.5   308370 
Quantile  0.75  309871 
Quantile  0.975 314579 
Mean            667491 
Stdev           6333.76 
Quantile  0.025 653294 
Quantile  0.25  664331 
Quantile  0.5   667640 
Quantile  0.75  670844 
Quantile  0.975 680273 
Mean            367678 
Stdev           3477 
Quantile  0.025 360271 
Quantile  0.25  365877 
Quantile  0.5   367666 
Quantile  0.75  369456 
Quantile  0.975 375073 
Mean            286826 
Stdev           2714.16 
Quantile  0.025 281109 
Quantile  0.25  285410 
Quantile  0.5   286801 
Quantile  0.75  288202 
Quantile  0.975 292663 
Mean            294020 
Stdev           2787.75 
Quantile  0.025 288289 
Quantile  0.25  292545 
Quantile  0.5   293961 
Quantile  0.75  295408 
Quantile  0.975 300156 
Mean            208912 
Stdev           1976.72 
Quantile  0.025 204739 
Quantile  0.25  207883 
Quantile  0.5   208897 
Quantile  0.75  209916 
Quantile  0.975 213154 
Mean            216234 
Stdev           2046.65 
Quantile  0.025 211945 
Quantile  0.25  215163 
Quantile  0.5   216210 
Quantile  0.75  217268 
Quantile  0.975 220658 
Mean            259961 
Stdev           2463.26 
Quantile  0.025 254979 
Quantile  0.25  258643 
Quantile  0.5   259889 
Quantile  0.75  261175 
Quantile  0.975 265462 
Mean            216173 
Stdev           2045.66 
Quantile  0.025 211795 
Quantile  0.25  215118 
Quantile  0.5   216172 
Quantile  0.75  217222 
Quantile  0.975 220505 
Mean            365159 
Stdev           3457.48 
Quantile  0.025 357916 
Quantile  0.25  363350 
Quantile  0.5   365118 
Quantile  0.75  366905 
Quantile  0.975 372635 
Mean            199620 
Stdev           1890.34 
Quantile  0.025 195641 
Quantile  0.25  198634 
Quantile  0.5   199602 
Quantile  0.75  200577 
Quantile  0.975 203689 
Mean            584277 
Stdev           5560.44 
Quantile  0.025 571553 
Quantile  0.25  581550 
Quantile  0.5   584472 
Quantile  0.75  587263 
Quantile  0.975 595244 
Mean            304222 
Stdev           2880.67 
Quantile  0.025 298145 
Quantile  0.25  302722 
Quantile  0.5   304198 
Quantile  0.75  305683 
Quantile  0.975 310410 
Mean            211627 
Stdev           2002.09 
Quantile  0.025 207421 
Quantile  0.25  210580 
Quantile  0.5   211606 
Quantile  0.75  212640 
Quantile  0.975 215943 
Mean            227163 
Stdev           2148.91 
Quantile  0.025 222550 
Quantile  0.25  226056 
Quantile  0.5   227164 
Quantile  0.75  228267 
Quantile  0.975 231699 
Mean            355774 
Stdev           3370.35 
Quantile  0.025 348586 
Quantile  0.25  354032 
Quantile  0.5   355765 
Quantile  0.75  357496 
Quantile  0.975 362938 
Mean            586735 
Stdev           5551.2 
Quantile  0.025 574715 
Quantile  0.25  583893 
Quantile  0.5   586764 
Quantile  0.75  589606 
Quantile  0.975 598351 
Mean            259919 
Stdev           2465.35 
Quantile  0.025 254870 
Quantile  0.25  258611 
Quantile  0.5   259862 
Quantile  0.75  261143 
Quantile  0.975 265364 
Mean            280157 
Stdev           2660.54 
Quantile  0.025 274749 
Quantile  0.25  278739 
Quantile  0.5   280085 
Quantile  0.75  281469 
Quantile  0.975 286075 
Mean            317954 
Stdev           3006.69 
Quantile  0.025 311510 
Quantile  0.25  316404 
Quantile  0.5   317954 
Quantile  0.75  319498 
Quantile  0.975 324311 
Mean            317323 
Stdev           3005.5 
Quantile  0.025 310684 
Quantile  0.25  315806 
Quantile  0.5   317370 
Quantile  0.75  318899 
Quantile  0.975 323484 
Mean            244833 
Stdev           2319.8 
Quantile  0.025 240113 
Quantile  0.25  243597 
Quantile  0.5   244772 
Quantile  0.75  245980 
Quantile  0.975 249986 
Mean            359860 
Stdev           3411.73 
Quantile  0.025 352866 
Quantile  0.25  358051 
Quantile  0.5   359783 
Quantile  0.75  361556 
Quantile  0.975 367389 
Mean            416833 
Stdev           3945.92 
Quantile  0.025 408364 
Quantile  0.25  414801 
Quantile  0.5   416835 
Quantile  0.75  418860 
Quantile  0.975 425166 
Mean            352984 
Stdev           3340.45 
Quantile  0.025 345875 
Quantile  0.25  351253 
Quantile  0.5   352971 
Quantile  0.75  354689 
Quantile  0.975 360097 
Mean            252876 
Stdev           2391.3 
Quantile  0.025 247769 
Quantile  0.25  251640 
Quantile  0.5   252871 
Quantile  0.75  254101 
Quantile  0.975 257949 
Mean            255868 
Stdev           2421.28 
Quantile  0.025 250684 
Quantile  0.25  254618 
Quantile  0.5   255866 
Quantile  0.75  257109 
Quantile  0.975 260993 
Mean            251438 
Stdev           2385.02 
Quantile  0.025 246586 
Quantile  0.25  250167 
Quantile  0.5   251374 
Quantile  0.75  252616 
Quantile  0.975 256738 
Mean            173339 
Stdev           1648.13 
Quantile  0.025 170051 
Quantile  0.25  172451 
Quantile  0.5   173279 
Quantile  0.75  174141 
Quantile  0.975 177066 
Mean            340465 
Stdev           3219.58 
Quantile  0.025 333586 
Quantile  0.25  338801 
Quantile  0.5   340460 
Quantile  0.75  342115 
Quantile  0.975 347292 
Mean            361510 
Stdev           3426.39 
Quantile  0.025 354256 
Quantile  0.25  359730 
Quantile  0.5   361487 
Quantile  0.75  363251 
Quantile  0.975 368846 
Mean            290403 
Stdev           2753.41 
Quantile  0.025 284719 
Quantile  0.25  288950 
Quantile  0.5   290350 
Quantile  0.75  291778 
Quantile  0.975 296440 
Mean            244432 
Stdev           2314.14 
Quantile  0.025 239573 
Quantile  0.25  243223 
Quantile  0.5   244408 
Quantile  0.75  245603 
Quantile  0.975 249425 
Mean            263025 
Stdev           2489.85 
Quantile  0.025 257782 
Quantile  0.25  261726 
Quantile  0.5   263002 
Quantile  0.75  264287 
Quantile  0.975 268382 
Mean            524576 
Stdev           4966.87 
Quantile  0.025 513559 
Quantile  0.25  522077 
Quantile  0.5   524666 
Quantile  0.75  527190 
Quantile  0.975 534711 
Mean            347796 
Stdev           3294.83 
Quantile  0.025 340952 
Quantile  0.25  346063 
Quantile  0.5   347743 
Quantile  0.75  349449 
Quantile  0.975 354979 
Mean            405851 
Stdev           3839.36 
Quantile  0.025 397484 
Quantile  0.25  403893 
Quantile  0.5   405883 
Quantile  0.75  407846 
Quantile  0.975 413832 
Mean            360089 
Stdev           3414.9 
Quantile  0.025 353130 
Quantile  0.25  358271 
Quantile  0.5   360001 
Quantile  0.75  361778 
Quantile  0.975 367665 
Mean            345708 
Stdev           3271.96 
Quantile  0.025 338782 
Quantile  0.25  344008 
Quantile  0.5   345687 
Quantile  0.75  347373 
Quantile  0.975 352712 
Mean            287342 
Stdev           2720.5 
Quantile  0.025 281635 
Quantile  0.25  285919 
Quantile  0.5   287311 
Quantile  0.75  288716 
Quantile  0.975 293216 
Mean            337327 
Stdev           3195.38 
Quantile  0.025 330742 
Quantile  0.25  335638 
Quantile  0.5   337263 
Quantile  0.75  338922 
Quantile  0.975 344343 
Mean            373406 
Stdev           3532.79 
Quantile  0.025 365922 
Quantile  0.25  371570 
Quantile  0.5   373384 
Quantile  0.75  375204 
Quantile  0.975 380962 
Mean            309294 
Stdev           2926.05 
Quantile  0.025 303079 
Quantile  0.25  307776 
Quantile  0.5   309279 
Quantile  0.75  310786 
Quantile  0.975 315536 
Mean            444031 
Stdev           4202.99 
Quantile  0.025 435163 
Quantile  0.25  441841 
Quantile  0.5   443996 
Quantile  0.75  446164 
Quantile  0.975 453057 
Mean            632901 
Stdev           5990.56 
Quantile  0.025 619896 
Quantile  0.25  629840 
Quantile  0.5   632940 
Quantile  0.75  636004 
Quantile  0.975 645405 
Mean            334026 
Stdev           3158.46 
Quantile  0.025 327367 
Quantile  0.25  332379 
Quantile  0.5   333999 
Quantile  0.75  335629 
Quantile  0.975 340812 
Mean            353090 
Stdev           3339.16 
Quantile  0.025 345993 
Quantile  0.25  351358 
Quantile  0.5   353075 
Quantile  0.75  354794 
Quantile  0.975 360208 
Mean            548026 
Stdev           5187.03 
Quantile  0.025 537062 
Quantile  0.25  545327 
Quantile  0.5   547987 
Quantile  0.75  550661 
Quantile  0.975 559145 
Mean            329781 
Stdev           3120.84 
Quantile  0.025 323135 
Quantile  0.25  328166 
Quantile  0.5   329771 
Quantile  0.75  331376 
Quantile  0.975 336422 
Mean            420882 
Stdev           3980.63 
Quantile  0.025 412262 
Quantile  0.25  418843 
Quantile  0.5   420902 
Quantile  0.75  422941 
Quantile  0.975 429211 
Mean            326097 
Stdev           3084 
Quantile  0.025 319553 
Quantile  0.25  324496 
Quantile  0.5   326081 
Quantile  0.75  327669 
Quantile  0.975 332682 
Mean            297246 
Stdev           2813.38 
Quantile  0.025 291349 
Quantile  0.25  295774 
Quantile  0.5   297214 
Quantile  0.75  298667 
Quantile  0.975 303326 
Mean            351084 
Stdev           3321.29 
Quantile  0.025 344015 
Quantile  0.25  349363 
Quantile  0.5   351071 
Quantile  0.75  352780 
Quantile  0.975 358155 
Mean            217280 
Stdev           2055.42 
Quantile  0.025 212891 
Quantile  0.25  216217 
Quantile  0.5   217276 
Quantile  0.75  218332 
Quantile  0.975 221642 
Mean            249268 
Stdev           2357.17 
Quantile  0.025 244222 
Quantile  0.25  248052 
Quantile  0.5   249267 
Quantile  0.75  250478 
Quantile  0.975 254258 
Mean            229436 
Stdev           2172.38 
Quantile  0.025 224884 
Quantile  0.25  228300 
Quantile  0.5   229411 
Quantile  0.75  230533 
Quantile  0.975 234132 
Mean            223875 
Stdev           2117.79 
Quantile  0.025 219346 
Quantile  0.25  222781 
Quantile  0.5   223872 
Quantile  0.75  224960 
Quantile  0.975 228362 
Mean            371306 
Stdev           3517.92 
Quantile  0.025 363854 
Quantile  0.25  369480 
Quantile  0.5   371284 
Quantile  0.75  373095 
Quantile  0.975 378833 
Mean            223755 
Stdev           2117.91 
Quantile  0.025 219346 
Quantile  0.25  222642 
Quantile  0.5   223723 
Quantile  0.75  224820 
Quantile  0.975 228362 
Mean            384422 
Stdev           3635.42 
Quantile  0.025 376447 
Quantile  0.25  382577 
Quantile  0.5   384466 
Quantile  0.75  386321 
Quantile  0.975 391926 
Mean            466530 
Stdev           4413.34 
Quantile  0.025 456915 
Quantile  0.25  464279 
Quantile  0.5   466567 
Quantile  0.75  468823 
Quantile  0.975 475707 
Mean            255724 
Stdev           2426.07 
Quantile  0.025 250765 
Quantile  0.25  254435 
Quantile  0.5   255665 
Quantile  0.75  256926 
Quantile  0.975 261092 
Mean            366744 
Stdev           3471.95 
Quantile  0.025 359447 
Quantile  0.25  364931 
Quantile  0.5   366709 
Quantile  0.75  368501 
Quantile  0.975 374227 
Mean            347815 
Stdev           3293.21 
Quantile  0.025 340853 
Quantile  0.25  346102 
Quantile  0.5   347791 
Quantile  0.75  349488 
Quantile  0.975 354874 
Mean            264938 
Stdev           2509.28 
Quantile  0.025 259675 
Quantile  0.25  263627 
Quantile  0.5   264910 
Quantile  0.75  266206 
Quantile  0.975 270358 
Mean            196718 
Stdev           1861.49 
Quantile  0.025 192797 
Quantile  0.25  195747 
Quantile  0.5   196701 
Quantile  0.75  197661 
Quantile  0.975 200721 
Mean            202679 
Stdev           1915.94 
Quantile  0.025 198585 
Quantile  0.25  201689 
Quantile  0.5   202676 
Quantile  0.75  203661 
Quantile  0.975 206741 
Mean            235089 
Stdev           2224.57 
Quantile  0.025 230505 
Quantile  0.25  233912 
Quantile  0.5   235044 
Quantile  0.75  236200 
Quantile  0.975 239973 
Mean            278044 
Stdev           2637.59 
Quantile  0.025 272665 
Quantile  0.25  276641 
Quantile  0.5   277977 
Quantile  0.75  279349 
Quantile  0.975 283893 
Mean            489241 
Stdev           4629.47 
Quantile  0.025 479484 
Quantile  0.25  486827 
Quantile  0.5   489200 
Quantile  0.75  491589 
Quantile  0.975 499193 
Mean            352292 
Stdev           3332.12 
Quantile  0.025 345063 
Quantile  0.25  350588 
Quantile  0.5   352312 
Quantile  0.75  354018 
Quantile  0.975 359250 
Mean            369273 
Stdev           3499.11 
Quantile  0.025 362112 
Quantile  0.25  367415 
Quantile  0.5   369191 
Quantile  0.75  371010 
Quantile  0.975 377006 
Mean            216155 
Stdev           2054.67 
Quantile  0.025 212030 
Quantile  0.25  215053 
Quantile  0.5   216087 
Quantile  0.75  217160 
Quantile  0.975 220776 
Mean            383573 
Stdev           3629.48 
Quantile  0.025 375685 
Quantile  0.25  381719 
Quantile  0.5   383599 
Quantile  0.75  385455 
Quantile  0.975 391140 
Mean            337242 
Stdev           3191.58 
Quantile  0.025 330536 
Quantile  0.25  335575 
Quantile  0.5   337209 
Quantile  0.75  338857 
Quantile  0.975 344123 
Mean            618422 
Stdev           5856.28 
Quantile  0.025 605882 
Quantile  0.25  615402 
Quantile  0.5   618417 
Quantile  0.75  621424 
Quantile  0.975 630818 
Mean            333145 
Stdev           3151.8 
Quantile  0.025 326528 
Quantile  0.25  331497 
Quantile  0.5   333111 
Quantile  0.75  334739 
Quantile  0.975 339945 
Mean            426599 
Stdev           4037.29 
Quantile  0.025 417735 
Quantile  0.25  424552 
Quantile  0.5   426649 
Quantile  0.75  428708 
Quantile  0.975 434927 
Mean            165674 
Stdev           1572.39 
Quantile  0.025 162450 
Quantile  0.25  164841 
Quantile  0.5   165638 
Quantile  0.75  166454 
Quantile  0.975 169144 
Mean            455532 
Stdev           4307.68 
Quantile  0.025 446295 
Quantile  0.25  453311 
Quantile  0.5   455533 
Quantile  0.75  457745 
Quantile  0.975 464635 
Mean            447198 
Stdev           4233.79 
Quantile  0.025 438216 
Quantile  0.25  445001 
Quantile  0.5   447175 
Quantile  0.75  449355 
Quantile  0.975 456241 
Mean            608121 
Stdev           5801.07 
Quantile  0.025 594662 
Quantile  0.25  605310 
Quantile  0.5   608371 
Quantile  0.75  611265 
Quantile  0.975 619380 
Mean            226495 
Stdev           2142.73 
Quantile  0.025 221943 
Quantile  0.25  225383 
Quantile  0.5   226485 
Quantile  0.75  227588 
Quantile  0.975 231065 
Mean            385114 
Stdev           3647.59 
Quantile  0.025 377398 
Quantile  0.25  383218 
Quantile  0.5   385088 
Quantile  0.75  386967 
Quantile  0.975 392928 
Mean            744553 
Stdev           7058.33 
Quantile  0.025 728766 
Quantile  0.25  741025 
Quantile  0.5   744712 
Quantile  0.75  748287 
Quantile  0.975 758828 
Mean            325693 
Stdev           3080.12 
Quantile  0.025 319152 
Quantile  0.25  324095 
Quantile  0.5   325678 
Quantile  0.75  327265 
Quantile  0.975 332264 
Mean            296325 
Stdev           2804.01 
Quantile  0.025 290417 
Quantile  0.25  294863 
Quantile  0.5   296300 
Quantile  0.75  297747 
Quantile  0.975 302354 
Mean            419722 
Stdev           3970.53 
Quantile  0.025 411184 
Quantile  0.25  417679 
Quantile  0.5   419728 
Quantile  0.75  421765 
Quantile  0.975 428089 
Mean            397681 
Stdev           3763.44 
Quantile  0.025 389672 
Quantile  0.25  395732 
Quantile  0.5   397667 
Quantile  0.75  399603 
Quantile  0.975 405695 
Mean            169366 
Stdev           1615.5 
Quantile  0.025 166188 
Quantile  0.25  168490 
Quantile  0.5   169297 
Quantile  0.75  170143 
Quantile  0.975 173065 
Mean            280531 
Stdev           2656.65 
Quantile  0.025 274944 
Quantile  0.25  279145 
Quantile  0.5   280505 
Quantile  0.75  281876 
Quantile  0.975 286255 
Mean            166176 
Stdev           1575.09 
Quantile  0.025 162950 
Quantile  0.25  165340 
Quantile  0.5   166140 
Quantile  0.75  166958 
Quantile  0.975 169655 
Mean            214021 
Stdev           2025.26 
Quantile  0.025 209757 
Quantile  0.25  212964 
Quantile  0.5   214002 
Quantile  0.75  215047 
Quantile  0.975 218379 
Mean            315900 
Stdev           2990.75 
Quantile  0.025 309556 
Quantile  0.25  314347 
Quantile  0.5   315883 
Quantile  0.75  317423 
Quantile  0.975 322289 
Mean            426244 
Stdev           4030.85 
Quantile  0.025 417461 
Quantile  0.25  424188 
Quantile  0.5   426278 
Quantile  0.75  428338 
Quantile  0.975 434624 
Mean            275515 
Stdev           2608.73 
Quantile  0.025 270006 
Quantile  0.25  274158 
Quantile  0.5   275495 
Quantile  0.75  276840 
Quantile  0.975 281112 
Mean            239540 
Stdev           2285.68 
Quantile  0.025 235052 
Quantile  0.25  238299 
Quantile  0.5   239440 
Quantile  0.75  240638 
Quantile  0.975 244782 
Mean            364863 
Stdev           3453.94 
Quantile  0.025 357481 
Quantile  0.25  363079 
Quantile  0.5   364857 
Quantile  0.75  366631 
Quantile  0.975 372187 
Mean            145657 
Stdev           1411.25 
Quantile  0.025 143043 
Quantile  0.25  144869 
Quantile  0.5   145555 
Quantile  0.75  146301 
Quantile  0.975 149050 
Mean            272782 
Stdev           2581.79 
Quantile  0.025 267430 
Quantile  0.25  271421 
Quantile  0.5   272738 
Quantile  0.75  274076 
Quantile  0.975 278419 
Mean            274847 
Stdev           2608.59 
Quantile  0.025 269535 
Quantile  0.25  273459 
Quantile  0.5   274779 
Quantile  0.75  276136 
Quantile  0.975 280639 
Mean            269246 
Stdev           2547.97 
Quantile  0.025 263760 
Quantile  0.25  267936 
Quantile  0.5   269251 
Quantile  0.75  270558 
Quantile  0.975 274609 
Mean            251405 
Stdev           2379.42 
Quantile  0.025 246367 
Quantile  0.25  250168 
Quantile  0.5   251390 
Quantile  0.75  252616 
Quantile  0.975 256497 
Mean            320254 
Stdev           3029.5 
Quantile  0.025 313759 
Quantile  0.25  318692 
Quantile  0.5   320253 
Quantile  0.75  321809 
Quantile  0.975 326657 
Mean            308197 
Stdev           2921.34 
Quantile  0.025 302146 
Quantile  0.25  306658 
Quantile  0.5   308145 
Quantile  0.75  309659 
Quantile  0.975 314583 
Mean            314212 
Stdev           2973.94 
Quantile  0.025 307922 
Quantile  0.25  312665 
Quantile  0.5   314191 
Quantile  0.75  315723 
Quantile  0.975 320583 
Mean            243049 
Stdev           2300.87 
Quantile  0.025 238244 
Quantile  0.25  241843 
Quantile  0.5   243019 
Quantile  0.75  244209 
Quantile  0.975 248039 
Mean            454607 
Stdev           4301.46 
Quantile  0.025 445196 
Quantile  0.25  452421 
Quantile  0.5   454653 
Quantile  0.75  456849 
Quantile  0.975 463512 
Mean            340556 
Stdev           3225.7 
Quantile  0.025 333799 
Quantile  0.25  338869 
Quantile  0.5   340518 
Quantile  0.75  342184 
Quantile  0.975 347532 
Mean            506676 
Stdev           4795.12 
Quantile  0.025 496320 
Quantile  0.25  504217 
Quantile  0.5   506694 
Quantile  0.75  509150 
Quantile  0.975 516737 
Mean            154333 
Stdev           1469.15 
Quantile  0.025 151417 
Quantile  0.25  153540 
Quantile  0.5   154277 
Quantile  0.75  155045 
Quantile  0.975 157670 
Mean            185752 
Stdev           1784.13 
Quantile  0.025 182342 
Quantile  0.25  184770 
Quantile  0.5   185650 
Quantile  0.75  186589 
Quantile  0.975 189937 
Mean            290446 
Stdev           2751.01 
Quantile  0.025 284681 
Quantile  0.25  289007 
Quantile  0.5   290414 
Quantile  0.75  291835 
Quantile  0.975 296393 
Mean            214432 
Stdev           2030.94 
Quantile  0.025 210172 
Quantile  0.25  213370 
Quantile  0.5   214409 
Quantile  0.75  215458 
Quantile  0.975 218819 
Mean            176742 
Stdev           1674.65 
Quantile  0.025 173254 
Quantile  0.25  175863 
Quantile  0.5   176717 
Quantile  0.75  177584 
Quantile  0.975 180384 
Mean            286333 
Stdev           2709.71 
Quantile  0.025 280636 
Quantile  0.25  284918 
Quantile  0.5   286306 
Quantile  0.75  287705 
Quantile  0.975 292172 
Mean            286270 
Stdev           2711.53 
Quantile  0.025 280625 
Quantile  0.25  284846 
Quantile  0.5   286229 
Quantile  0.75  287633 
Quantile  0.975 292168 
Mean            317949 
Stdev           3010.37 
Quantile  0.025 311637 
Quantile  0.25  316374 
Quantile  0.5   317914 
Quantile  0.75  319469 
Quantile  0.975 324453 
Mean            257895 
Stdev           2441.52 
Quantile  0.025 252708 
Quantile  0.25  256629 
Quantile  0.5   257883 
Quantile  0.75  259139 
Quantile  0.975 263103 
Mean            666396 
Stdev           6304.52 
Quantile  0.025 653019 
Quantile  0.25  663123 
Quantile  0.5   666362 
Quantile  0.75  669609 
Quantile  0.975 679859 
Mean            238843 
Stdev           2259.25 
Quantile  0.025 234117 
Quantile  0.25  237659 
Quantile  0.5   238815 
Quantile  0.75  239983 
Quantile  0.975 243734 
Mean            252485 
Stdev           2393.64 
Quantile  0.025 247537 
Quantile  0.25  251223 
Quantile  0.5   252441 
Quantile  0.75  253682 
Quantile  0.975 257727 
Mean            720955 
Stdev           6828.67 
Quantile  0.025 705806 
Quantile  0.25  717519 
Quantile  0.5   721078 
Quantile  0.75  724547 
Quantile  0.975 734888 
Mean            393394 
Stdev           3719.09 
Quantile  0.025 385498 
Quantile  0.25  391463 
Quantile  0.5   393375 
Quantile  0.75  395291 
Quantile  0.975 401330 
Mean            334783 
Stdev           3168.19 
Quantile  0.025 328038 
Quantile  0.25  333142 
Quantile  0.5   334771 
Quantile  0.75  336401 
Quantile  0.975 341527 
Mean            244097 
Stdev           2308.48 
Quantile  0.025 239197 
Quantile  0.25  242899 
Quantile  0.5   244085 
Quantile  0.75  245274 
Quantile  0.975 249025 
Mean            266509 
Stdev           2526.89 
Quantile  0.025 261313 
Quantile  0.25  265171 
Quantile  0.5   266455 
Quantile  0.75  267767 
Quantile  0.975 272070 
Mean            372669 
Stdev           3532.35 
Quantile  0.025 364830 
Quantile  0.25  370893 
Quantile  0.5   372733 
Quantile  0.75  374526 
Quantile  0.975 379875 
Mean            288136 
Stdev           2728.78 
Quantile  0.025 282402 
Quantile  0.25  286711 
Quantile  0.5   288108 
Quantile  0.75  289516 
Quantile  0.975 294020 
Mean            230440 
Stdev           2182.8 
Quantile  0.025 225872 
Quantile  0.25  229298 
Quantile  0.5   230413 
Quantile  0.75  231541 
Quantile  0.975 235165 
Mean            404852 
Stdev           3825.86 
Quantile  0.025 396517 
Quantile  0.25  402900 
Quantile  0.5   404884 
Quantile  0.75  406841 
Quantile  0.975 412805 
Mean            271444 
Stdev           2569.25 
Quantile  0.025 266062 
Quantile  0.25  270099 
Quantile  0.5   271414 
Quantile  0.75  272741 
Quantile  0.975 276999 
Mean            251802 
Stdev           2388.25 
Quantile  0.025 246890 
Quantile  0.25  250539 
Quantile  0.5   251752 
Quantile  0.75  252991 
Quantile  0.975 257057 
Mean            465925 
Stdev           4410.04 
Quantile  0.025 456609 
Quantile  0.25  463629 
Quantile  0.5   465891 
Quantile  0.75  468165 
Quantile  0.975 475384 
Mean            575296 
Stdev           5469.97 
Quantile  0.025 562795 
Quantile  0.25  572609 
Quantile  0.5   575484 
Quantile  0.75  578232 
Quantile  0.975 586098 
Mean            292977 
Stdev           2773.06 
Quantile  0.025 286911 
Quantile  0.25  291567 
Quantile  0.5   293006 
Quantile  0.75  294421 
Quantile  0.975 298719 
Mean            252671 
Stdev           2393.78 
Quantile  0.025 247702 
Quantile  0.25  251412 
Quantile  0.5   252632 
Quantile  0.75  253872 
Quantile  0.975 257893 
Mean            336722 
Stdev           3186.09 
Quantile  0.025 329998 
Quantile  0.25  335062 
Quantile  0.5   336696 
Quantile  0.75  338340 
Quantile  0.975 343562 
Mean            278854 
Stdev           2640.66 
Quantile  0.025 273335 
Quantile  0.25  277470 
Quantile  0.5   278820 
Quantile  0.75  280185 
Quantile  0.975 284577 
Mean            390875 
Stdev           3700.6 
Quantile  0.025 383290 
Quantile  0.25  388911 
Quantile  0.5   390791 
Quantile  0.75  392715 
Quantile  0.975 399039 
Mean            509427 
Stdev           4819.03 
Quantile  0.025 499097 
Quantile  0.25  506943 
Quantile  0.5   509427 
Quantile  0.75  511902 
Quantile  0.975 519614 
Mean            390039 
Stdev           3693.53 
Quantile  0.025 382262 
Quantile  0.25  388112 
Quantile  0.5   390004 
Quantile  0.75  391909 
Quantile  0.975 397987 
Mean            239631 
Stdev           2267.07 
Quantile  0.025 234871 
Quantile  0.25  238446 
Quantile  0.5   239607 
Quantile  0.75  240779 
Quantile  0.975 244522 
Mean            267025 
Stdev           2526.79 
Quantile  0.025 261703 
Quantile  0.25  265707 
Quantile  0.5   267002 
Quantile  0.75  268306 
Quantile  0.975 272460 
Mean            236827 
Stdev           2246.97 
Quantile  0.025 232251 
Quantile  0.25  235630 
Quantile  0.5   236768 
Quantile  0.75  237937 
Quantile  0.975 241816 
Mean            356658 
Stdev           3374.6 
Quantile  0.025 349589 
Quantile  0.25  354892 
Quantile  0.5   356618 
Quantile  0.75  358363 
Quantile  0.975 363954 
Mean            216414 
Stdev           2081.31 
Quantile  0.025 212466 
Quantile  0.25  215265 
Quantile  0.5   216288 
Quantile  0.75  217385 
Quantile  0.975 221325 
Mean            323807 
Stdev           3088.27 
Quantile  0.025 317716 
Quantile  0.25  322134 
Quantile  0.5   323678 
Quantile  0.75  325295 
Quantile  0.975 330863 
Mean            543397 
Stdev           5156.07 
Quantile  0.025 532906 
Quantile  0.25  540651 
Quantile  0.5   543261 
Quantile  0.75  545944 
Quantile  0.975 554854 
Mean            329117 
Stdev           3112.57 
Quantile  0.025 322391 
Quantile  0.25  327520 
Quantile  0.5   329129 
Quantile  0.75  330724 
Quantile  0.975 335643 
Mean            388702 
Stdev           3681.89 
Quantile  0.025 380597 
Quantile  0.25  386840 
Quantile  0.5   388753 
Quantile  0.75  390628 
Quantile  0.975 396277 
Mean            328754 
Stdev           3107.72 
Quantile  0.025 322094 
Quantile  0.25  327150 
Quantile  0.5   328753 
Quantile  0.75  330350 
Quantile  0.975 335324 
Mean            642787 
Stdev           6097 
Quantile  0.025 629089 
Quantile  0.25  639750 
Quantile  0.5   642939 
Quantile  0.75  646022 
Quantile  0.975 655059 
Mean            276675 
Stdev           2618.24 
Quantile  0.025 271236 
Quantile  0.25  275297 
Quantile  0.5   276633 
Quantile  0.75  277990 
Quantile  0.975 282381 
Mean            301608 
Stdev           2853.71 
Quantile  0.025 295419 
Quantile  0.25  300149 
Quantile  0.5   301626 
Quantile  0.75  303086 
Quantile  0.975 307570 
Mean            354425 
Stdev           3352.47 
Quantile  0.025 347353 
Quantile  0.25  352678 
Quantile  0.5   354397 
Quantile  0.75  356127 
Quantile  0.975 361624 
Mean            438327 
Stdev           4151.35 
Quantile  0.025 429715 
Quantile  0.25  436142 
Quantile  0.5   438258 
Quantile  0.75  440409 
Quantile  0.975 447387 
Mean            726768 
Stdev           6876.69 
Quantile  0.025 711835 
Quantile  0.25  723254 
Quantile  0.5   726814 
Quantile  0.75  730331 
Quantile  0.975 741116 
Mean            319943 
Stdev           3025.54 
Quantile  0.025 313441 
Quantile  0.25  318385 
Quantile  0.5   319947 
Quantile  0.75  321500 
Quantile  0.975 326322 
Mean            276057 
Stdev           2612.49 
Quantile  0.025 270604 
Quantile  0.25  274687 
Quantile  0.5   276022 
Quantile  0.75  277374 
Quantile  0.975 281724 
Mean            184584 
Stdev           1804.43 
Quantile  0.025 181322 
Quantile  0.25  183568 
Quantile  0.5   184434 
Quantile  0.75  185389 
Quantile  0.975 189000 
Mean            312155 
Stdev           2961.69 
Quantile  0.025 306106 
Quantile  0.25  310581 
Quantile  0.5   312082 
Quantile  0.75  313622 
Quantile  0.975 318713 
Mean            280938 
Stdev           2662.63 
Quantile  0.025 275500 
Quantile  0.25  279523 
Quantile  0.5   280873 
Quantile  0.75  282258 
Quantile  0.975 286833 
Mean            243413 
Stdev           2300.68 
Quantile  0.025 238553 
Quantile  0.25  242214 
Quantile  0.5   243395 
Quantile  0.75  244582 
Quantile  0.975 248346 
Mean            319581 
Stdev           3021.11 
Quantile  0.025 313147 
Quantile  0.25  318016 
Quantile  0.5   319571 
Quantile  0.75  321126 
Quantile  0.975 326008 
Mean            286141 
Stdev           2702.45 
Quantile  0.025 280473 
Quantile  0.25  284726 
Quantile  0.5   286111 
Quantile  0.75  287509 
Quantile  0.975 291975 
Mean            365009 
Stdev           3450.97 
Quantile  0.025 357704 
Quantile  0.25  363214 
Quantile  0.5   364986 
Quantile  0.75  366766 
Quantile  0.975 372394 
Mean            279503 
Stdev           2657.12 
Quantile  0.025 274173 
Quantile  0.25  278077 
Quantile  0.5   279415 
Quantile  0.75  280802 
Quantile  0.975 285484 
Mean            416928 
Stdev           3940.87 
Quantile  0.025 408615 
Quantile  0.25  414874 
Quantile  0.5   416896 
Quantile  0.75  418930 
Quantile  0.975 425389 
Mean            287631 
Stdev           2722.9 
Quantile  0.025 281904 
Quantile  0.25  286210 
Quantile  0.5   287605 
Quantile  0.75  289010 
Quantile  0.975 293496 
Mean            285622 
Stdev           2703.63 
Quantile  0.025 279922 
Quantile  0.25  284213 
Quantile  0.5   285599 
Quantile  0.75  286994 
Quantile  0.975 291432 
Mean            619681 
Stdev           5880.06 
Quantile  0.025 606434 
Quantile  0.25  616759 
Quantile  0.5   619836 
Quantile  0.75  622807 
Quantile  0.975 631480 
Mean            336563 
Stdev           3185.9 
Quantile  0.025 329900 
Quantile  0.25  334893 
Quantile  0.5   336522 
Quantile  0.75  338169 
Quantile  0.975 343462 
Mean            289047 
Stdev           2736.81 
Quantile  0.025 283312 
Quantile  0.25  287615 
Quantile  0.5   289014 
Quantile  0.75  290428 
Quantile  0.975 294963 
Mean            337166 
Stdev           3192.9 
Quantile  0.025 330495 
Quantile  0.25  335493 
Quantile  0.5   337124 
Quantile  0.75  338775 
Quantile  0.975 344087 
Mean            256865 
Stdev           2431.4 
Quantile  0.025 251807 
Quantile  0.25  255587 
Quantile  0.5   256828 
Quantile  0.75  258087 
Quantile  0.975 262157 
Mean            482641 
Stdev           4562.22 
Quantile  0.025 473029 
Quantile  0.25  480261 
Quantile  0.5   482601 
Quantile  0.75  484957 
Quantile  0.975 492449 
Mean            378118 
Stdev           3578.9 
Quantile  0.025 370555 
Quantile  0.25  376256 
Quantile  0.5   378091 
Quantile  0.75  379936 
Quantile  0.975 385792 
Mean            390976 
Stdev           3714.57 
Quantile  0.025 383511 
Quantile  0.25  388983 
Quantile  0.5   390855 
Quantile  0.75  392794 
Quantile  0.975 399323 
Mean            795361 
Stdev           7539.39 
Quantile  0.025 778561 
Quantile  0.25  791581 
Quantile  0.5   795514 
Quantile  0.75  799338 
Quantile  0.975 810672 
Mean            538295 
Stdev           5102.17 
Quantile  0.025 527767 
Quantile  0.25  535601 
Quantile  0.5   538196 
Quantile  0.75  540842 
Quantile  0.975 549487 
Mean            305961 
Stdev           2901.63 
Quantile  0.025 300049 
Quantile  0.25  304417 
Quantile  0.5   305886 
Quantile  0.75  307396 
Quantile  0.975 312400 
Mean            261883 
Stdev           2478.27 
Quantile  0.025 256601 
Quantile  0.25  260600 
Quantile  0.5   261875 
Quantile  0.75  263150 
Quantile  0.975 267153 
Mean            297794 
Stdev           2818.27 
Quantile  0.025 291809 
Quantile  0.25  296333 
Quantile  0.5   297781 
Quantile  0.75  299231 
Quantile  0.975 303808 
Mean            291947 
Stdev           2764.26 
Quantile  0.025 286155 
Quantile  0.25  290501 
Quantile  0.5   291914 
Quantile  0.75  293342 
Quantile  0.975 297923 
Mean            244524 
Stdev           2319.45 
Quantile  0.025 239791 
Quantile  0.25  243291 
Quantile  0.5   244466 
Quantile  0.75  245672 
Quantile  0.975 249665 
Mean            282671 
Stdev           2676.63 
Quantile  0.025 277103 
Quantile  0.25  281265 
Quantile  0.5   282630 
Quantile  0.75  284016 
Quantile  0.975 288497 
Mean            428634 
Stdev           4054.5 
Quantile  0.025 420088 
Quantile  0.25  426520 
Quantile  0.5   428599 
Quantile  0.75  430692 
Quantile  0.975 437347 
Mean            314823 
Stdev           2978.94 
Quantile  0.025 308540 
Quantile  0.25  313270 
Quantile  0.5   314798 
Quantile  0.75  316335 
Quantile  0.975 321221 
Mean            260082 
Stdev           2461.22 
Quantile  0.025 254835 
Quantile  0.25  258809 
Quantile  0.5   260075 
Quantile  0.75  261341 
Quantile  0.975 265314 
Mean            303166 
Stdev           2870.2 
Quantile  0.025 297179 
Quantile  0.25  301660 
Quantile  0.5   303126 
Quantile  0.75  304611 
Quantile  0.975 309398 
Mean            258608 
Stdev           2448.52 
Quantile  0.025 253428 
Quantile  0.25  257335 
Quantile  0.5   258592 
Quantile  0.75  259853 
Quantile  0.975 263853 
Mean            227075 
Stdev           2146.56 
Quantile  0.025 222487 
Quantile  0.25  225966 
Quantile  0.5   227072 
Quantile  0.75  228176 
Quantile  0.975 231625 
Mean            242040 
Stdev           2291.78 
Quantile  0.025 237241 
Quantile  0.25  240841 
Quantile  0.5   242013 
Quantile  0.75  243197 
Quantile  0.975 246997 
Mean            325003 
Stdev           3078.55 
Quantile  0.025 318630 
Quantile  0.25  323380 
Quantile  0.5   324949 
Quantile  0.75  326544 
Quantile  0.975 331734 
Mean            297588 
Stdev           2817.22 
Quantile  0.025 291594 
Quantile  0.25  296128 
Quantile  0.5   297576 
Quantile  0.75  299026 
Quantile  0.975 303589 
Mean            322723 
Stdev           3052.03 
Quantile  0.025 316135 
Quantile  0.25  321157 
Quantile  0.5   322734 
Quantile  0.75  324298 
Quantile  0.975 329129 
Mean            358388 
Stdev           3390.45 
Quantile  0.025 351180 
Quantile  0.25  356630 
Quantile  0.5   358373 
Quantile  0.75  360119 
Quantile  0.975 365614 
Mean            313840 
Stdev           2969.09 
Quantile  0.025 307604 
Quantile  0.25  312288 
Quantile  0.5   313809 
Quantile  0.75  315343 
Quantile  0.975 320243 
Mean            348598 
Stdev           3295.91 
Quantile  0.025 341455 
Quantile  0.25  346910 
Quantile  0.5   348616 
Quantile  0.75  350304 
Quantile  0.975 355488 
Mean            330524 
Stdev           3123.09 
Quantile  0.025 323937 
Quantile  0.25  328895 
Quantile  0.5   330498 
Quantile  0.75  332110 
Quantile  0.975 337230 
Mean            214761 
Stdev           2033.91 
Quantile  0.025 210539 
Quantile  0.25  213690 
Quantile  0.5   214728 
Quantile  0.75  215781 
Quantile  0.975 219197 
Mean            387146 
Stdev           3663.57 
Quantile  0.025 379294 
Quantile  0.25  385257 
Quantile  0.5   387145 
Quantile  0.75  389026 
Quantile  0.975 394893 
Mean            287574 
Stdev           2721.35 
Quantile  0.025 281763 
Quantile  0.25  286167 
Quantile  0.5   287568 
Quantile  0.75  288967 
Quantile  0.975 293350 
Mean            337276 
Stdev           3191.73 
Quantile  0.025 330472 
Quantile  0.25  335625 
Quantile  0.5   337267 
Quantile  0.75  338908 
Quantile  0.975 344061 
Mean            280154 
Stdev           2647.4 
Quantile  0.025 274471 
Quantile  0.25  278789 
Quantile  0.5   280156 
Quantile  0.75  281516 
Quantile  0.975 285741 
Mean            200307 
Stdev           1895.86 
Quantile  0.025 196298 
Quantile  0.25  199321 
Quantile  0.5   200294 
Quantile  0.75  201271 
Quantile  0.975 204369 
Mean            278896 
Stdev           2637.47 
Quantile  0.025 273148 
Quantile  0.25  277551 
Quantile  0.5   278919 
Quantile  0.75  280267 
Quantile  0.975 284378 
Mean            261141 
Stdev           2473.45 
Quantile  0.025 255958 
Quantile  0.25  259848 
Quantile  0.5   261112 
Quantile  0.75  262390 
Quantile  0.975 266489 
Mean            399287 
Stdev           3780.04 
Quantile  0.025 391251 
Quantile  0.25  397328 
Quantile  0.5   399271 
Quantile  0.75  401216 
Quantile  0.975 407345 
Mean            629276 
Stdev           5956.69 
Quantile  0.025 616158 
Quantile  0.25  626263 
Quantile  0.5   629360 
Quantile  0.75  632394 
Quantile  0.975 641524 
Mean            335499 
Stdev           3180.94 
Quantile  0.025 328902 
Quantile  0.25  333825 
Quantile  0.5   335445 
Quantile  0.75  337092 
Quantile  0.975 342444 
Mean            400163 
Stdev           3786.58 
Quantile  0.025 391927 
Quantile  0.25  398230 
Quantile  0.5   400192 
Quantile  0.75  402128 
Quantile  0.975 408050 
Mean            383871 
Stdev           3636.26 
Quantile  0.025 376265 
Quantile  0.25  381967 
Quantile  0.5   383825 
Quantile  0.75  385704 
Quantile  0.975 391746 
Mean            436038 
Stdev           4126.7 
Quantile  0.025 426895 
Quantile  0.25  433959 
Quantile  0.5   436110 
Quantile  0.75  438208 
Quantile  0.975 444467 
Mean            369963 
Stdev           3501.81 
Quantile  0.025 362630 
Quantile  0.25  368130 
Quantile  0.5   369920 
Quantile  0.75  371730 
Quantile  0.975 377537 
Mean            567262 
Stdev           5370.38 
Quantile  0.025 555664 
Quantile  0.25  564508 
Quantile  0.5   567282 
Quantile  0.75  570033 
Quantile  0.975 578532 
Mean            518866 
Stdev           4913.5 
Quantile  0.025 508092 
Quantile  0.25  516373 
Quantile  0.5   518923 
Quantile  0.75  521428 
Quantile  0.975 529017 
Mean            435186 
Stdev           4115.77 
Quantile  0.025 426286 
Quantile  0.25  433076 
Quantile  0.5   435204 
Quantile  0.75  437313 
Quantile  0.975 443810 
Mean            326775 
Stdev           3099.37 
Quantile  0.025 320314 
Quantile  0.25  325150 
Quantile  0.5   326730 
Quantile  0.75  328332 
Quantile  0.975 333511 
Mean            229475 
Stdev           2174.6 
Quantile  0.025 224977 
Quantile  0.25  228329 
Quantile  0.5   229436 
Quantile  0.75  230563 
Quantile  0.975 234234 
Mean            242503 
Stdev           2308.44 
Quantile  0.025 237911 
Quantile  0.25  241258 
Quantile  0.5   242416 
Quantile  0.75  243623 
Quantile  0.975 247737 
Mean            269007 
Stdev           2546.93 
Quantile  0.025 263616 
Quantile  0.25  267683 
Quantile  0.5   268990 
Quantile  0.75  270302 
Quantile  0.975 274459 
Mean            294448 
Stdev           2792.89 
Quantile  0.025 288748 
Quantile  0.25  292964 
Quantile  0.5   294379 
Quantile  0.75  295831 
Quantile  0.975 300636 
Mean            236643 
Stdev           2240.05 
Quantile  0.025 231958 
Quantile  0.25  235470 
Quantile  0.5   236615 
Quantile  0.75  237773 
Quantile  0.975 241494 
Mean            271411 
Stdev           2567.95 
Quantile  0.025 265981 
Quantile  0.25  270075 
Quantile  0.5   271392 
Quantile  0.75  272716 
Quantile  0.975 276913 
Mean            276340 
Stdev           2613.58 
Quantile  0.025 270859 
Quantile  0.25  274973 
Quantile  0.5   276311 
Quantile  0.75  277662 
Quantile  0.975 281984 
Mean            413870 
Stdev           3917.45 
Quantile  0.025 405669 
Quantile  0.25  411819 
Quantile  0.5   413823 
Quantile  0.75  415848 
Quantile  0.975 422345 
Mean            468024 
Stdev           4424.52 
Quantile  0.025 458378 
Quantile  0.25  465768 
Quantile  0.5   468063 
Quantile  0.75  470325 
Quantile  0.975 477216 
Mean            799140 
Stdev           7565.22 
Quantile  0.025 782853 
Quantile  0.25  795253 
Quantile  0.5   799156 
Quantile  0.75  803035 
Quantile  0.975 815067 
Mean            629872 
Stdev           5976.67 
Quantile  0.025 616409 
Quantile  0.25  626901 
Quantile  0.5   630030 
Quantile  0.75  633049 
Quantile  0.975 641866 
Mean            613385 
Stdev           5803.12 
Quantile  0.025 601205 
Quantile  0.25  610351 
Quantile  0.5   613322 
Quantile  0.75  616321 
Quantile  0.975 625908 
Mean            174822 
Stdev           1726.98 
Quantile  0.025 171777 
Quantile  0.25  173840 
Quantile  0.5   174658 
Quantile  0.75  175574 
Quantile  0.975 179122 
Mean            374797 
Stdev           3547.07 
Quantile  0.025 366971 
Quantile  0.25  373005 
Quantile  0.5   374851 
Quantile  0.75  376657 
Quantile  0.975 382075 
Mean            478626 
Stdev           4537.57 
Quantile  0.025 468445 
Quantile  0.25  476363 
Quantile  0.5   478736 
Quantile  0.75  481032 
Quantile  0.975 487771 
Mean            161315 
Stdev           1533.24 
Quantile  0.025 158234 
Quantile  0.25  160492 
Quantile  0.5   161264 
Quantile  0.75  162064 
Quantile  0.975 164761 
Mean            286498 
Stdev           2712.38 
Quantile  0.025 280743 
Quantile  0.25  285091 
Quantile  0.5   286484 
Quantile  0.75  287880 
Quantile  0.975 292291 
Mean            225679 
Stdev           2137.41 
Quantile  0.025 221265 
Quantile  0.25  224550 
Quantile  0.5   225638 
Quantile  0.75  226747 
Quantile  0.975 230363 
Mean            282237 
Stdev           2669.09 
Quantile  0.025 276482 
Quantile  0.25  280866 
Quantile  0.5   282245 
Quantile  0.75  283613 
Quantile  0.975 287846 
Mean            297032 
Stdev           2813.88 
Quantile  0.025 291112 
Quantile  0.25  295564 
Quantile  0.5   297005 
Quantile  0.75  298456 
Quantile  0.975 303093 
Mean            445059 
Stdev           4216.8 
Quantile  0.025 436354 
Quantile  0.25  442832 
Quantile  0.5   444977 
Quantile  0.75  447165 
Quantile  0.975 454304 
Mean            263853 
Stdev           2497.82 
Quantile  0.025 258636 
Quantile  0.25  262544 
Quantile  0.5   263820 
Quantile  0.75  265112 
Quantile  0.975 269270 
Mean            432131 
Stdev           4083.54 
Quantile  0.025 423370 
Quantile  0.25  430026 
Quantile  0.5   432133 
Quantile  0.75  434231 
Quantile  0.975 440754 
Mean            304379 
Stdev           2878.71 
Quantile  0.025 298093 
Quantile  0.25  302913 
Quantile  0.5   304407 
Quantile  0.75  305877 
Quantile  0.975 310350 
Mean            288772 
Stdev           2742.33 
Quantile  0.025 283214 
Quantile  0.25  287308 
Quantile  0.5   288694 
Quantile  0.75  290122 
Quantile  0.975 294888 
Mean            251402 
Stdev           2381.9 
Quantile  0.025 246503 
Quantile  0.25  250141 
Quantile  0.5   251351 
Quantile  0.75  252588 
Quantile  0.975 256642 
Mean            308424 
Stdev           2917.4 
Quantile  0.025 302273 
Quantile  0.25  306903 
Quantile  0.5   308399 
Quantile  0.75  309904 
Quantile  0.975 314692 
Mean            387231 
Stdev           3661.85 
Quantile  0.025 379362 
Quantile  0.25  385345 
Quantile  0.5   387235 
Quantile  0.75  389115 
Quantile  0.975 394952 
Mean            473315 
Stdev           4481.59 
Quantile  0.025 463984 
Quantile  0.25  470960 
Quantile  0.5   473248 
Quantile  0.75  475568 
Quantile  0.975 483061 
Mean            229043 
Stdev           2174.99 
Quantile  0.025 224645 
Quantile  0.25  227881 
Quantile  0.5   228979 
Quantile  0.75  230112 
Quantile  0.975 233903 
Mean            229948 
Stdev           2176.89 
Quantile  0.025 225403 
Quantile  0.25  228806 
Quantile  0.5   229918 
Quantile  0.75  231044 
Quantile  0.975 234670 
Mean            219011 
Stdev           2071.51 
Quantile  0.025 214636 
Quantile  0.25  217933 
Quantile  0.5   218996 
Quantile  0.75  220064 
Quantile  0.975 223454 
Mean            198381 
Stdev           1875.98 
Quantile  0.025 194374 
Quantile  0.25  197411 
Quantile  0.5   198377 
Quantile  0.75  199342 
Quantile  0.975 202361 
Mean            387753 
Stdev           3669.74 
Quantile  0.025 380049 
Quantile  0.25  385834 
Quantile  0.5   387713 
Quantile  0.75  389608 
Quantile  0.975 395671 
Mean            419156 
Stdev           3969.3 
Quantile  0.025 410670 
Quantile  0.25  417107 
Quantile  0.5   419150 
Quantile  0.75  421188 
Quantile  0.975 427572 
Mean            376523 
Stdev           3563.93 
Quantile  0.025 369000 
Quantile  0.25  374668 
Quantile  0.5   376495 
Quantile  0.75  378333 
Quantile  0.975 384173 
Mean            445880 
Stdev           4216.96 
Quantile  0.025 436758 
Quantile  0.25  443719 
Quantile  0.5   445900 
Quantile  0.75  448060 
Quantile  0.975 454712 
Mean            319938 
Stdev           3028.38 
Quantile  0.025 313272 
Quantile  0.25  318405 
Quantile  0.5   319980 
Quantile  0.75  321522 
Quantile  0.975 326168 
Mean            285549 
Stdev           2702.21 
Quantile  0.025 279593 
Quantile  0.25  284183 
Quantile  0.5   285589 
Quantile  0.75  286965 
Quantile  0.975 291100 
Mean            466731 
Stdev           4418.32 
Quantile  0.025 457106 
Quantile  0.25  464479 
Quantile  0.5   466767 
Quantile  0.75  469025 
Quantile  0.975 475920 
Mean            392826 
Stdev           3721.03 
Quantile  0.025 385123 
Quantile  0.25  390864 
Quantile  0.5   392759 
Quantile  0.75  394688 
Quantile  0.975 400963 
Mean            304997 
Stdev           2886.47 
Quantile  0.025 298871 
Quantile  0.25  303499 
Quantile  0.5   304982 
Quantile  0.75  306468 
Quantile  0.975 311160 
Mean            550825 
Stdev           5213.55 
Quantile  0.025 539807 
Quantile  0.25  548113 
Quantile  0.5   550787 
Quantile  0.75  553475 
Quantile  0.975 562003 
Mean            519218 
Stdev           4911.54 
Quantile  0.025 508530 
Quantile  0.25  516712 
Quantile  0.5   519257 
Quantile  0.75  521768 
Quantile  0.975 529443 
Mean            415667 
Stdev           3931.67 
Quantile  0.025 407130 
Quantile  0.25  413658 
Quantile  0.5   415693 
Quantile  0.75  417705 
Quantile  0.975 423870 
Mean            338528 
Stdev           3205.61 
Quantile  0.025 331772 
Quantile  0.25  336858 
Quantile  0.5   338500 
Quantile  0.75  340153 
Quantile  0.975 345420 
Mean            341038 
Stdev           3227.58 
Quantile  0.025 333951 
Quantile  0.25  339402 
Quantile  0.5   341079 
Quantile  0.75  342724 
Quantile  0.975 347695 
Mean            364073 
Stdev           3450.04 
Quantile  0.025 357016 
Quantile  0.25  362240 
Quantile  0.5   363991 
Quantile  0.75  365785 
Quantile  0.975 371700 
Mean            458859 
Stdev           4340.72 
Quantile  0.025 449293 
Quantile  0.25  456663 
Quantile  0.5   458922 
Quantile  0.75  461133 
Quantile  0.975 467776 
Mean            617648 
Stdev           5846.48 
Quantile  0.025 605320 
Quantile  0.25  614601 
Quantile  0.5   617598 
Quantile  0.75  620613 
Quantile  0.975 630210 
Mean            449221 
Stdev           4246.56 
Quantile  0.025 440098 
Quantile  0.25  447034 
Quantile  0.5   449226 
Quantile  0.75  451406 
Quantile  0.975 458177 
Mean            326659 
Stdev           3091.98 
Quantile  0.025 319891 
Quantile  0.25  325088 
Quantile  0.5   326693 
Quantile  0.75  328270 
Quantile  0.975 333058 
Mean            235577 
Stdev           2240.1 
Quantile  0.025 231090 
Quantile  0.25  234373 
Quantile  0.5   235500 
Quantile  0.75  236669 
Quantile  0.975 240626 
Mean            248409 
Stdev           2350.3 
Quantile  0.025 243438 
Quantile  0.25  247186 
Quantile  0.5   248393 
Quantile  0.75  249604 
Quantile  0.975 253444 
Mean            291430 
Stdev           2757.81 
Quantile  0.025 285327 
Quantile  0.25  290039 
Quantile  0.5   291476 
Quantile  0.75  292879 
Quantile  0.975 297070 
Mean            362171 
Stdev           3423.67 
Quantile  0.025 354868 
Quantile  0.25  360399 
Quantile  0.5   362162 
Quantile  0.75  363924 
Quantile  0.975 369443 
Mean            187627 
Stdev           1776.44 
Quantile  0.025 183901 
Quantile  0.25  186699 
Quantile  0.5   187608 
Quantile  0.75  188525 
Quantile  0.975 191464 
Mean            453438 
Stdev           4292.2 
Quantile  0.025 444392 
Quantile  0.25  451201 
Quantile  0.5   453400 
Quantile  0.75  455614 
Quantile  0.975 462665 
Mean            199934 
Stdev           1892.48 
Quantile  0.025 195973 
Quantile  0.25  198944 
Quantile  0.5   199911 
Quantile  0.75  200890 
Quantile  0.975 204029 
Mean            321577 
Stdev           3041.58 
Quantile  0.025 315243 
Quantile  0.25  319978 
Quantile  0.5   321532 
Quantile  0.75  323108 
Quantile  0.975 328189 
Mean            200011 
Stdev           1891.8 
Quantile  0.025 196015 
Quantile  0.25  199026 
Quantile  0.5   199996 
Quantile  0.75  200972 
Quantile  0.975 204069 
Mean            230410 
Stdev           2180.06 
Quantile  0.025 225803 
Quantile  0.25  229276 
Quantile  0.5   230394 
Quantile  0.75  231518 
Quantile  0.975 235084 
Mean            271821 
Stdev           2573.9 
Quantile  0.025 266394 
Quantile  0.25  270480 
Quantile  0.5   271799 
Quantile  0.75  273126 
Quantile  0.975 277352 
Mean            179467 
Stdev           1699.99 
Quantile  0.025 175963 
Quantile  0.25  178568 
Quantile  0.5   179433 
Quantile  0.75  180315 
Quantile  0.975 183199 
Mean            168348 
Stdev           1602.26 
Quantile  0.025 165170 
Quantile  0.25  167482 
Quantile  0.5   168285 
Quantile  0.75  169124 
Quantile  0.975 171990 
Mean            328834 
Stdev           3110.7 
Quantile  0.025 322289 
Quantile  0.25  327210 
Quantile  0.5   328804 
Quantile  0.75  330410 
Quantile  0.975 335530 
Mean            250636 
Stdev           2371.19 
Quantile  0.025 245513 
Quantile  0.25  249421 
Quantile  0.5   250646 
Quantile  0.75  251861 
Quantile  0.975 255609 
Mean            234612 
Stdev           2222.99 
Quantile  0.025 229915 
Quantile  0.25  233456 
Quantile  0.5   234595 
Quantile  0.75  235740 
Quantile  0.975 239381 
Mean            429376 
Stdev           4071.12 
Quantile  0.025 420258 
Quantile  0.25  427343 
Quantile  0.5   429471 
Quantile  0.75  431532 
Quantile  0.975 437598 
Mean            518654 
Stdev           4907.08 
Quantile  0.025 508028 
Quantile  0.25  516142 
Quantile  0.5   518680 
Quantile  0.75  521192 
Quantile  0.975 528922 
Mean            373526 
Stdev           3538.58 
Quantile  0.025 366210 
Quantile  0.25  371659 
Quantile  0.5   373460 
Quantile  0.75  375295 
Quantile  0.975 381273 
Mean            258267 
Stdev           2448.2 
Quantile  0.025 253175 
Quantile  0.25  256980 
Quantile  0.5   258229 
Quantile  0.75  259495 
Quantile  0.975 263598 
Mean            237757 
Stdev           2257 
Quantile  0.025 233206 
Quantile  0.25  236549 
Quantile  0.5   237688 
Quantile  0.75  238865 
Quantile  0.975 242813 
Mean            271205 
Stdev           2571.93 
Quantile  0.025 265908 
Quantile  0.25  269845 
Quantile  0.5   271152 
Quantile  0.75  272487 
Quantile  0.975 276857 
Mean            296977 
Stdev           2808.37 
Quantile  0.025 290987 
Quantile  0.25  295524 
Quantile  0.5   296970 
Quantile  0.75  298414 
Quantile  0.975 302943 
Mean            266733 
Stdev           2530.83 
Quantile  0.025 261566 
Quantile  0.25  265388 
Quantile  0.5   266671 
Quantile  0.75  267986 
Quantile  0.975 272339 
Mean            355466 
Stdev           3365 
Quantile  0.025 348279 
Quantile  0.25  353728 
Quantile  0.5   355460 
Quantile  0.75  357189 
Quantile  0.975 362606 
Mean            317179 
Stdev           2998.02 
Quantile  0.025 310941 
Quantile  0.25  315602 
Quantile  0.5   317134 
Quantile  0.75  318688 
Quantile  0.975 323700 
Mean            196755 
Stdev           1862.7 
Quantile  0.025 192888 
Quantile  0.25  195775 
Quantile  0.5   196725 
Quantile  0.75  197690 
Quantile  0.975 200817 
Mean            303291 
Stdev           2872.28 
Quantile  0.025 297186 
Quantile  0.25  301803 
Quantile  0.5   303278 
Quantile  0.75  304756 
Quantile  0.975 309416 
Mean            256608 
Stdev           2428.3 
Quantile  0.025 251320 
Quantile  0.25  255370 
Quantile  0.5   256628 
Quantile  0.75  257869 
Quantile  0.975 261660 
Mean            189886 
Stdev           1799.11 
Quantile  0.025 186201 
Quantile  0.25  188932 
Quantile  0.5   189845 
Quantile  0.75  190780 
Quantile  0.975 193858 
Mean            234603 
Stdev           2234.99 
Quantile  0.025 230168 
Quantile  0.25  233397 
Quantile  0.5   234517 
Quantile  0.75  235686 
Quantile  0.975 239682 
Mean            348646 
Stdev           3294.49 
Quantile  0.025 341430 
Quantile  0.25  346971 
Quantile  0.5   348683 
Quantile  0.75  350365 
Quantile  0.975 355456 
Mean            843826 
Stdev           8013.51 
Quantile  0.025 825673 
Quantile  0.25  839861 
Quantile  0.5   844062 
Quantile  0.75  848101 
Quantile  0.975 859809 
Mean            634943 
Stdev           6014.36 
Quantile  0.025 621505 
Quantile  0.25  631932 
Quantile  0.5   635075 
Quantile  0.75  638124 
Quantile  0.975 647118 
Mean            357373 
Stdev           3383.15 
Quantile  0.025 350307 
Quantile  0.25  355598 
Quantile  0.5   357327 
Quantile  0.75  359077 
Quantile  0.975 364709 
Mean            412938 
Stdev           3908.93 
Quantile  0.025 404706 
Quantile  0.25  410900 
Quantile  0.5   412903 
Quantile  0.75  414920 
Quantile  0.975 421347 
Mean            321139 
Stdev           3040.21 
Quantile  0.025 314749 
Quantile  0.25  319551 
Quantile  0.5   321108 
Quantile  0.75  322677 
Quantile  0.975 327692 
Mean            527163 
Stdev           4987.38 
Quantile  0.025 516379 
Quantile  0.25  524607 
Quantile  0.5   527185 
Quantile  0.75  529740 
Quantile  0.975 537615 
Mean            425407 
Stdev           4028.1 
Quantile  0.025 417024 
Quantile  0.25  423290 
Quantile  0.5   425345 
Quantile  0.75  427431 
Quantile  0.975 434171 
Mean            605794 
Stdev           5734.75 
Quantile  0.025 593470 
Quantile  0.25  602843 
Quantile  0.5   605800 
Quantile  0.75  608742 
Quantile  0.975 617889 
Mean            452868 
Stdev           4288.26 
Quantile  0.025 443426 
Quantile  0.25  450699 
Quantile  0.5   452928 
Quantile  0.75  455112 
Quantile  0.975 461687 
Mean            380472 
Stdev           3601.76 
Quantile  0.025 372790 
Quantile  0.25  378609 
Quantile  0.5   380462 
Quantile  0.75  382313 
Quantile  0.975 388125 
Mean            556811 
Stdev           5324.11 
Quantile  0.025 544349 
Quantile  0.25  554252 
Quantile  0.5   557067 
Quantile  0.75  559712 
Quantile  0.975 567037 
Mean            435093 
Stdev           4119.22 
Quantile  0.025 426045 
Quantile  0.25  433005 
Quantile  0.5   435145 
Quantile  0.75  437244 
Quantile  0.975 443587 
Mean            417455 
Stdev           3950.26 
Quantile  0.025 408860 
Quantile  0.25  415439 
Quantile  0.5   417485 
Quantile  0.75  419505 
Quantile  0.975 425680 
Mean            416683 
Stdev           3940.5 
Quantile  0.025 408300 
Quantile  0.25  414640 
Quantile  0.5   416667 
Quantile  0.75  418695 
Quantile  0.975 425075 
Mean            233135 
Stdev           2208.89 
Quantile  0.025 228502 
Quantile  0.25  231980 
Quantile  0.5   233110 
Quantile  0.75  234250 
Quantile  0.975 237907 
Mean            353634 
Stdev           3356.43 
Quantile  0.025 346117 
Quantile  0.25  351959 
Quantile  0.5   353712 
Quantile  0.75  355410 
Quantile  0.975 360415 
Mean            213942 
Stdev           2033.12 
Quantile  0.025 209843 
Quantile  0.25  212854 
Quantile  0.5   213879 
Quantile  0.75  214939 
Quantile  0.975 218497 
Mean            335122 
Stdev           3167.03 
Quantile  0.025 328290 
Quantile  0.25  333495 
Quantile  0.5   335132 
Quantile  0.75  336757 
Quantile  0.975 341773 
Mean            232500 
Stdev           2200.4 
Quantile  0.025 227833 
Quantile  0.25  231358 
Quantile  0.5   232488 
Quantile  0.75  233621 
Quantile  0.975 237201 
Mean            226446 
Stdev           2142.97 
Quantile  0.025 221972 
Quantile  0.25  225322 
Quantile  0.5   226418 
Quantile  0.75  227526 
Quantile  0.975 231094 
Mean            293999 
Stdev           2793.37 
Quantile  0.025 288374 
Quantile  0.25  292503 
Quantile  0.5   293911 
Quantile  0.75  295368 
Quantile  0.975 300265 
Mean            229571 
Stdev           2175.26 
Quantile  0.025 225065 
Quantile  0.25  228425 
Quantile  0.5   229533 
Quantile  0.75  230660 
Quantile  0.975 234325 
Mean            371671 
Stdev           3515.78 
Quantile  0.025 364022 
Quantile  0.25  369877 
Quantile  0.5   371698 
Quantile  0.75  373496 
Quantile  0.975 378992 
Mean            296524 
Stdev           2810.66 
Quantile  0.025 290749 
Quantile  0.25  295036 
Quantile  0.5   296463 
Quantile  0.75  297923 
Quantile  0.975 302713 
Mean            292383 
Stdev           2765.94 
Quantile  0.025 286491 
Quantile  0.25  290950 
Quantile  0.5   292373 
Quantile  0.75  293796 
Quantile  0.975 298266 
Mean            349361 
Stdev           3308.08 
Quantile  0.025 342437 
Quantile  0.25  347629 
Quantile  0.5   349320 
Quantile  0.75  351030 
Quantile  0.975 356520 
Mean            620734 
Stdev           5934.95 
Quantile  0.025 606863 
Quantile  0.25  617879 
Quantile  0.5   621015 
Quantile  0.75  623966 
Quantile  0.975 632154 
Mean            310084 
Stdev           2944.73 
Quantile  0.025 304116 
Quantile  0.25  308513 
Quantile  0.5   310001 
Quantile  0.75  311534 
Quantile  0.975 316651 
Mean            328799 
Stdev           3109.56 
Quantile  0.025 322203 
Quantile  0.25  327184 
Quantile  0.5   328782 
Quantile  0.75  330384 
Quantile  0.975 335440 
Mean            434868 
Stdev           4114.53 
Quantile  0.025 426246 
Quantile  0.25  432715 
Quantile  0.5   434821 
Quantile  0.75  436947 
Quantile  0.975 443760 
Mean            669591 
Stdev           6336.41 
Quantile  0.025 655990 
Quantile  0.25  666328 
Quantile  0.5   669595 
Quantile  0.75  672847 
Quantile  0.975 682969 
Mean            264142 
Stdev           2498.32 
Quantile  0.025 258907 
Quantile  0.25  262834 
Quantile  0.5   264113 
Quantile  0.75  265404 
Quantile  0.975 269541 
Mean            386223 
Stdev           3651.85 
Quantile  0.025 378514 
Quantile  0.25  384321 
Quantile  0.5   386195 
Quantile  0.75  388079 
Quantile  0.975 394060 
Mean            207198 
Stdev           1975.68 
Quantile  0.025 203304 
Quantile  0.25  206127 
Quantile  0.5   207115 
Quantile  0.75  208150 
Quantile  0.975 211714 
Mean            496656 
Stdev           4700.08 
Quantile  0.025 486773 
Quantile  0.25  494202 
Quantile  0.5   496609 
Quantile  0.75  499036 
Quantile  0.975 506782 
Mean            301637 
Stdev           2854.52 
Quantile  0.025 295489 
Quantile  0.25  300170 
Quantile  0.5   301644 
Quantile  0.75  303107 
Quantile  0.975 307643 
Mean            198027 
Stdev           1874.16 
Quantile  0.025 194093 
Quantile  0.25  197047 
Quantile  0.5   198007 
Quantile  0.75  198975 
Quantile  0.975 202071 
Mean            204224 
Stdev           1932.67 
Quantile  0.025 200160 
Quantile  0.25  203214 
Quantile  0.5   204204 
Quantile  0.75  205202 
Quantile  0.975 208388 
Mean            295333 
Stdev           2795.84 
Quantile  0.025 289453 
Quantile  0.25  293874 
Quantile  0.5   295305 
Quantile  0.75  296749 
Quantile  0.975 301356 
Mean            677934 
Stdev           6521.96 
Quantile  0.025 662386 
Quantile  0.25  674859 
Quantile  0.5   678321 
Quantile  0.75  681530 
Quantile  0.975 690181 
Mean            382112 
Stdev           3616.55 
Quantile  0.025 374459 
Quantile  0.25  380231 
Quantile  0.5   382087 
Quantile  0.75  383951 
Quantile  0.975 389856 
Mean            277321 
Stdev           2621.95 
Quantile  0.025 271643 
Quantile  0.25  275978 
Quantile  0.5   277335 
Quantile  0.75  278678 
Quantile  0.975 282806 
Mean            216977 
Stdev           2062.74 
Quantile  0.025 212868 
Quantile  0.25  215865 
Quantile  0.5   216902 
Quantile  0.75  217980 
Quantile  0.975 221647 
Mean            470373 
Stdev           4455.16 
Quantile  0.025 461034 
Quantile  0.25  468043 
Quantile  0.5   470322 
Quantile  0.75  472623 
Quantile  0.975 480002 
Mean            247811 
Stdev           2351.17 
Quantile  0.025 242992 
Quantile  0.25  246565 
Quantile  0.5   247758 
Quantile  0.75  248979 
Quantile  0.975 253001 
Mean            150895 
Stdev           1447.99 
Quantile  0.025 148114 
Quantile  0.25  150100 
Quantile  0.5   150816 
Quantile  0.75  151577 
Quantile  0.975 154278 
Mean            365840 
Stdev           3458.32 
Quantile  0.025 358416 
Quantile  0.25  364058 
Quantile  0.5   365842 
Quantile  0.75  367618 
Quantile  0.975 373139 
Mean            408327 
Stdev           3865.44 
Quantile  0.025 400020 
Quantile  0.25  406339 
Quantile  0.5   408332 
Quantile  0.75  410315 
Quantile  0.975 416479 
Mean            648146 
Stdev           6190.89 
Quantile  0.025 633747 
Quantile  0.25  645155 
Quantile  0.5   648421 
Quantile  0.75  651506 
Quantile  0.975 660129 
Mean            407382 
Stdev           3857.88 
Quantile  0.025 399323 
Quantile  0.25  405360 
Quantile  0.5   407330 
Quantile  0.75  409325 
Quantile  0.975 415746 
Mean            295189 
Stdev           2793.54 
Quantile  0.025 289248 
Quantile  0.25  293741 
Quantile  0.5   295177 
Quantile  0.75  296615 
Quantile  0.975 301141 
Mean            228828 
Stdev           2167.1 
Quantile  0.025 224274 
Quantile  0.25  227696 
Quantile  0.5   228806 
Quantile  0.75  229924 
Quantile  0.975 233500 
Mean            210055 
Stdev           1989.1 
Quantile  0.025 205919 
Quantile  0.25  209009 
Quantile  0.5   210024 
Quantile  0.75  211054 
Quantile  0.975 214387 
Mean            233774 
Stdev           2212.22 
Quantile  0.025 229044 
Quantile  0.25  232632 
Quantile  0.5   233771 
Quantile  0.75  234908 
Quantile  0.975 238463 
Mean            311807 
Stdev           2952.97 
Quantile  0.025 305705 
Quantile  0.25  310248 
Quantile  0.5   311752 
Quantile  0.75  313283 
Quantile  0.975 318275 
Mean            246040 
Stdev           2330.45 
Quantile  0.025 241158 
Quantile  0.25  244821 
Quantile  0.5   246012 
Quantile  0.75  247216 
Quantile  0.975 251079 
Mean            259833 
Stdev           2461.64 
Quantile  0.025 254662 
Quantile  0.25  258548 
Quantile  0.5   259807 
Quantile  0.75  261078 
Quantile  0.975 265142 
Mean            297455 
Stdev           2814.71 
Quantile  0.025 291569 
Quantile  0.25  295980 
Quantile  0.5   297419 
Quantile  0.75  298875 
Quantile  0.975 303551 
Mean            402797 
Stdev           3805.35 
Quantile  0.025 394723 
Quantile  0.25  400820 
Quantile  0.5   402777 
Quantile  0.75  404738 
Quantile  0.975 410921 
Mean            434390 
Stdev           4113.79 
Quantile  0.025 425801 
Quantile  0.25  432233 
Quantile  0.5   434334 
Quantile  0.75  436462 
Quantile  0.975 443314 
Mean            360627 
Stdev           3412.75 
Quantile  0.025 353279 
Quantile  0.25  358873 
Quantile  0.5   360634 
Quantile  0.75  362384 
Quantile  0.975 367810 
Mean            466702 
Stdev           4413.83 
Quantile  0.025 457345 
Quantile  0.25  464409 
Quantile  0.5   466677 
Quantile  0.75  468951 
Quantile  0.975 476135 
Mean            356191 
Stdev           3370.17 
Quantile  0.025 348879 
Quantile  0.25  354467 
Quantile  0.5   356211 
Quantile  0.75  357936 
Quantile  0.975 363229 
Mean            292833 
Stdev           2770.2 
Quantile  0.025 287007 
Quantile  0.25  291386 
Quantile  0.5   292805 
Quantile  0.75  294236 
Quantile  0.975 298799 
Mean            277182 
Stdev           2630.17 
Quantile  0.025 271877 
Quantile  0.25  275773 
Quantile  0.5   277101 
Quantile  0.75  278474 
Quantile  0.975 283071 
Mean            301676 
Stdev           2852.79 
Quantile  0.025 295589 
Quantile  0.25  300200 
Quantile  0.5   301668 
Quantile  0.75  303136 
Quantile  0.975 307734 
Mean            230228 
Stdev           2178.82 
Quantile  0.025 225650 
Quantile  0.25  229090 
Quantile  0.5   230206 
Quantile  0.75  231331 
Quantile  0.975 234926 
Mean            367919 
Stdev           3483.05 
Quantile  0.025 360409 
Quantile  0.25  366131 
Quantile  0.5   367929 
Quantile  0.75  369714 
Quantile  0.975 375241 
Mean            363906 
Stdev           3446.51 
Quantile  0.025 356755 
Quantile  0.25  362091 
Quantile  0.5   363848 
Quantile  0.75  365634 
Quantile  0.975 371427 
Mean            466630 
Stdev           4413.7 
Quantile  0.025 457314 
Quantile  0.25  464330 
Quantile  0.5   466595 
Quantile  0.75  468872 
Quantile  0.975 476103 
Mean            320721 
Stdev           3037.91 
Quantile  0.025 314308 
Quantile  0.25  319139 
Quantile  0.5   320696 
Quantile  0.75  322262 
Quantile  0.975 327243 
Mean            294165 
Stdev           2785.99 
Quantile  0.025 288354 
Quantile  0.25  292703 
Quantile  0.5   294126 
Quantile  0.75  295567 
Quantile  0.975 300215 
Mean            412564 
Stdev           3903.79 
Quantile  0.025 404082 
Quantile  0.25  410571 
Quantile  0.5   412592 
Quantile  0.75  414588 
Quantile  0.975 420704 
Mean            335962 
Stdev           3198.11 
Quantile  0.025 329572 
Quantile  0.25  334242 
Quantile  0.5   335849 
Quantile  0.75  337519 
Quantile  0.975 343186 
Mean            436743 
Stdev           4135.81 
Quantile  0.025 428036 
Quantile  0.25  434586 
Quantile  0.5   436704 
Quantile  0.75  438838 
Quantile  0.975 445644 
Mean            312571 
Stdev           2955.81 
Quantile  0.025 306260 
Quantile  0.25  311043 
Quantile  0.5   312565 
Quantile  0.75  314085 
Quantile  0.975 318843 
Mean            855744 
Stdev           8098.09 
Quantile  0.025 838334 
Quantile  0.25  851578 
Quantile  0.5   855756 
Quantile  0.75  859910 
Quantile  0.975 872815 
Mean            578983 
Stdev           5475.27 
Quantile  0.025 567194 
Quantile  0.25  576167 
Quantile  0.5   578995 
Quantile  0.75  581803 
Quantile  0.975 590505 
Mean            637345 
Stdev           6023.27 
Quantile  0.025 624339 
Quantile  0.25  634253 
Quantile  0.5   637367 
Quantile  0.75  640456 
Quantile  0.975 649982 
Mean            358542 
Stdev           3389.33 
Quantile  0.025 351269 
Quantile  0.25  356795 
Quantile  0.5   358544 
Quantile  0.75  360285 
Quantile  0.975 365698 
Mean            212846 
Stdev           2015.09 
Quantile  0.025 208642 
Quantile  0.25  211789 
Quantile  0.5   212818 
Quantile  0.75  213861 
Quantile  0.975 217220 
Mean            286188 
Stdev           2710.27 
Quantile  0.025 280423 
Quantile  0.25  284785 
Quantile  0.5   286177 
Quantile  0.75  287571 
Quantile  0.975 291963 
Mean            234496 
Stdev           2231.38 
Quantile  0.025 230056 
Quantile  0.25  233292 
Quantile  0.5   234412 
Quantile  0.75  235579 
Quantile  0.975 239554 
Mean            383040 
Stdev           3626.01 
Quantile  0.025 375258 
Quantile  0.25  381172 
Quantile  0.5   383041 
Quantile  0.75  384902 
Quantile  0.975 390697 
Mean            324741 
Stdev           3080.7 
Quantile  0.025 318419 
Quantile  0.25  323109 
Quantile  0.5   324673 
Quantile  0.75  326272 
Quantile  0.975 331534 
Mean            486125 
Stdev           4603.16 
Quantile  0.025 476549 
Quantile  0.25  483705 
Quantile  0.5   486054 
Quantile  0.75  488437 
Quantile  0.975 496145 
Mean            480571 
Stdev           4547.79 
Quantile  0.025 470881 
Quantile  0.25  478217 
Quantile  0.5   480556 
Quantile  0.75  482895 
Quantile  0.975 490244 
Mean            414111 
Stdev           3918.02 
Quantile  0.025 405820 
Quantile  0.25  412074 
Quantile  0.5   414085 
Quantile  0.75  416105 
Quantile  0.975 422500 
Mean            529394 
Stdev           5014.84 
Quantile  0.025 518297 
Quantile  0.25  526866 
Quantile  0.5   529477 
Quantile  0.75  532026 
Quantile  0.975 539654 
Mean            331753 
Stdev           3143.38 
Quantile  0.025 325166 
Quantile  0.25  330109 
Quantile  0.5   331716 
Quantile  0.75  333339 
Quantile  0.975 338549 
Mean            578905 
Stdev           5490.21 
Quantile  0.025 566523 
Quantile  0.25  576177 
Quantile  0.5   579054 
Quantile  0.75  581827 
Quantile  0.975 589907 
Mean            437235 
Stdev           4142.23 
Quantile  0.025 428200 
Quantile  0.25  435126 
Quantile  0.5   437271 
Quantile  0.75  439386 
Quantile  0.975 445840 
Mean            371464 
Stdev           3521.07 
Quantile  0.025 364092 
Quantile  0.25  369622 
Quantile  0.5   371421 
Quantile  0.75  373239 
Quantile  0.975 379084 
Mean            182946 
Stdev           1738.82 
Quantile  0.025 179477 
Quantile  0.25  182009 
Quantile  0.5   182883 
Quantile  0.75  183793 
Quantile  0.975 186878 
Mean            239777 
Stdev           2270.53 
Quantile  0.025 235078 
Quantile  0.25  238580 
Quantile  0.5   239737 
Quantile  0.75  240914 
Quantile  0.975 244743 
Mean            326498 
Stdev           3089.13 
Quantile  0.025 320094 
Quantile  0.25  324870 
Quantile  0.5   326445 
Quantile  0.75  328047 
Quantile  0.975 333243 
Mean            831117 
Stdev           7864.51 
Quantile  0.025 814012 
Quantile  0.25  827103 
Quantile  0.5   831176 
Quantile  0.75  835197 
Quantile  0.975 847499 
Mean            373227 
Stdev           3548.57 
Quantile  0.025 366041 
Quantile  0.25  371333 
Quantile  0.5   373124 
Quantile  0.75  374971 
Quantile  0.975 381149 
Mean            266562 
Stdev           2526.48 
Quantile  0.025 261296 
Quantile  0.25  265236 
Quantile  0.5   266525 
Quantile  0.75  267831 
Quantile  0.975 272052 
Mean            825819 
Stdev           7845.03 
Quantile  0.025 808013 
Quantile  0.25  821944 
Quantile  0.5   826059 
Quantile  0.75  830010 
Quantile  0.975 841433 
Mean            509030 
Stdev           4821.72 
Quantile  0.025 498998 
Quantile  0.25  506496 
Quantile  0.5   508956 
Quantile  0.75  511451 
Quantile  0.975 519525 
Mean            388967 
Stdev           3681.94 
Quantile  0.025 380957 
Quantile  0.25  387088 
Quantile  0.5   388994 
Quantile  0.75  390876 
Quantile  0.975 396636 
Mean            597720 
Stdev           5657.37 
Quantile  0.025 585451 
Quantile  0.25  594827 
Quantile  0.5   597754 
Quantile  0.75  600648 
Quantile  0.975 609541 
Mean            473603 
Stdev           4480.68 
Quantile  0.025 464105 
Quantile  0.25  471276 
Quantile  0.5   473577 
Quantile  0.75  475885 
Quantile  0.975 483180 
Mean            366464 
Stdev           3468.74 
Quantile  0.025 359202 
Quantile  0.25  364647 
Quantile  0.5   366421 
Quantile  0.75  368214 
Quantile  0.975 373969 
Mean            286265 
Stdev           2708.93 
Quantile  0.025 280466 
Quantile  0.25  284867 
Quantile  0.5   286262 
Quantile  0.75  287654 
Quantile  0.975 292000 
Mean            373413 
Stdev           3530.52 
Quantile  0.025 365946 
Quantile  0.25  371576 
Quantile  0.5   373389 
Quantile  0.75  375209 
Quantile  0.975 380975 
Mean            909492 
Stdev           8614.66 
Quantile  0.025 890310 
Quantile  0.25  905169 
Quantile  0.5   909664 
Quantile  0.75  914036 
Quantile  0.975 926998 
Mean            934776 
Stdev           8867.93 
Quantile  0.025 914881 
Quantile  0.25  930354 
Quantile  0.5   934989 
Quantile  0.75  939475 
Quantile  0.975 952654 
Mean            326115 
Stdev           3087.76 
Quantile  0.025 319589 
Quantile  0.25  324509 
Quantile  0.5   326092 
Quantile  0.75  327684 
Quantile  0.975 332735 
Mean            301979 
Stdev           2857.7 
Quantile  0.025 295887 
Quantile  0.25  300500 
Quantile  0.5   301971 
Quantile  0.75  303440 
Quantile  0.975 308054 
Mean            356438 
Stdev           3374.24 
Quantile  0.025 349339 
Quantile  0.25  354677 
Quantile  0.5   356405 
Quantile  0.75  358147 
Quantile  0.975 363704 
Mean            252545 
Stdev           2389.69 
Quantile  0.025 247546 
Quantile  0.25  251293 
Quantile  0.5   252516 
Quantile  0.75  253751 
Quantile  0.975 257718 
Mean            561542 
Stdev           5323.17 
Quantile  0.025 550616 
Quantile  0.25  558722 
Quantile  0.5   561425 
Quantile  0.75  564190 
Quantile  0.975 573275 
Mean            331164 
Stdev           3148.68 
Quantile  0.025 324882 
Quantile  0.25  329468 
Quantile  0.5   331051 
Quantile  0.75  332697 
Quantile  0.975 338284 
Mean            583450 
Stdev           5521.82 
Quantile  0.025 571513 
Quantile  0.25  580620 
Quantile  0.5   583473 
Quantile  0.75  586301 
Quantile  0.975 595025 
Mean            420332 
Stdev           3997.38 
Quantile  0.025 412350 
Quantile  0.25  418180 
Quantile  0.5   420189 
Quantile  0.75  422278 
Quantile  0.975 429365 
Mean            240976 
Stdev           2277.97 
Quantile  0.025 236110 
Quantile  0.25  239799 
Quantile  0.5   240972 
Quantile  0.75  242144 
Quantile  0.975 245807 
Mean            432884 
Stdev           4096.63 
Quantile  0.025 424172 
Quantile  0.25  430761 
Quantile  0.5   432867 
Quantile  0.75  434975 
Quantile  0.975 441614 
Mean            346847 
Stdev           3279.92 
Quantile  0.025 339811 
Quantile  0.25  345156 
Quantile  0.5   346848 
Quantile  0.75  348532 
Quantile  0.975 353775 
Mean            328484 
Stdev           3108.59 
Quantile  0.025 321867 
Quantile  0.25  326874 
Quantile  0.5   328472 
Quantile  0.75  330072 
Quantile  0.975 335102 
Mean            383059 
Stdev           3631.04 
Quantile  0.025 374997 
Quantile  0.25  381234 
Quantile  0.5   383126 
Quantile  0.75  384969 
Quantile  0.975 390462 
Mean            295699 
Stdev           2796.11 
Quantile  0.025 289617 
Quantile  0.25  294271 
Quantile  0.5   295720 
Quantile  0.75  297150 
Quantile  0.975 301522 
Mean            435337 
Stdev           4118.37 
Quantile  0.025 426360 
Quantile  0.25  433238 
Quantile  0.5   435373 
Quantile  0.75  437478 
Quantile  0.975 443896 
Mean            404180 
Stdev           3825.2 
Quantile  0.025 395739 
Quantile  0.25  402248 
Quantile  0.5   404239 
Quantile  0.75  406186 
Quantile  0.975 412028 
Mean            222164 
Stdev           2112.26 
Quantile  0.025 217930 
Quantile  0.25  221030 
Quantile  0.5   222093 
Quantile  0.75  223195 
Quantile  0.975 226921 
Mean            435177 
Stdev           4116.79 
Quantile  0.025 426411 
Quantile  0.25  433044 
Quantile  0.5   435162 
Quantile  0.75  437280 
Quantile  0.975 443937 
Mean            340632 
Stdev           3221.24 
Quantile  0.025 333699 
Quantile  0.25  338975 
Quantile  0.5   340638 
Quantile  0.75  342291 
Quantile  0.975 347413 
Mean            209792 
Stdev           1988.85 
Quantile  0.025 205712 
Quantile  0.25  208738 
Quantile  0.5   209747 
Quantile  0.75  210780 
Quantile  0.975 214178 
Mean            230917 
Stdev           2187.32 
Quantile  0.025 226303 
Quantile  0.25  229778 
Quantile  0.5   230898 
Quantile  0.75  232026 
Quantile  0.975 235616 
Mean            185011 
Stdev           1755.15 
Quantile  0.025 181454 
Quantile  0.25  184073 
Quantile  0.5   184961 
Quantile  0.75  185875 
Quantile  0.975 188925 
Mean            171521 
Stdev           1630.18 
Quantile  0.025 168245 
Quantile  0.25  170647 
Quantile  0.5   171468 
Quantile  0.75  172318 
Quantile  0.975 175184 
Mean            454831 
Stdev           4305.83 
Quantile  0.025 445296 
Quantile  0.25  452661 
Quantile  0.5   454904 
Quantile  0.75  457094 
Quantile  0.975 463632 
Mean            326896 
Stdev           3094.96 
Quantile  0.025 320477 
Quantile  0.25  325266 
Quantile  0.5   326844 
Quantile  0.75  328448 
Quantile  0.975 333651 
Mean            471450 
Stdev           4471.21 
Quantile  0.025 462342 
Quantile  0.25  469070 
Quantile  0.5   471334 
Quantile  0.75  473661 
Quantile  0.975 481374 
Mean            501761 
Stdev           4754.61 
Quantile  0.025 491918 
Quantile  0.25  499255 
Quantile  0.5   501676 
Quantile  0.75  504140 
Quantile  0.975 512159 
Mean            220686 
Stdev           2089.17 
Quantile  0.025 216384 
Quantile  0.25  219580 
Quantile  0.5   220643 
Quantile  0.75  221728 
Quantile  0.975 225276 
Mean            297517 
Stdev           2819.58 
Quantile  0.025 291713 
Quantile  0.25  296025 
Quantile  0.5   297459 
Quantile  0.75  298922 
Quantile  0.975 303715 
Mean            299751 
Stdev           2839.25 
Quantile  0.025 293805 
Quantile  0.25  298265 
Quantile  0.5   299716 
Quantile  0.75  301183 
Quantile  0.975 305893 
Mean            438600 
Stdev           4150.94 
Quantile  0.025 429796 
Quantile  0.25  436445 
Quantile  0.5   438576 
Quantile  0.75  440714 
Quantile  0.975 447468 
Mean            330588 
Stdev           3129.29 
Quantile  0.025 323783 
Quantile  0.25  328991 
Quantile  0.5   330611 
Quantile  0.75  332211 
Quantile  0.975 337109 
Mean            312533 
Stdev           2956.49 
Quantile  0.025 306312 
Quantile  0.25  310989 
Quantile  0.5   312504 
Quantile  0.75  314031 
Quantile  0.975 318897 
Mean            253925 
Stdev           2408.26 
Quantile  0.025 249004 
Quantile  0.25  252645 
Quantile  0.5   253866 
Quantile  0.75  255118 
Quantile  0.975 259256 
Mean            1134268 
Stdev           10908.1 
Quantile  0.025 1108288 
Quantile  0.25  1129119 
Quantile  0.5   1134908 
Quantile  0.75  1140279 
Quantile  0.975 1154776 
Mean            267731 
Stdev           2532.04 
Quantile  0.025 262259 
Quantile  0.25  266433 
Quantile  0.5   267742 
Quantile  0.75  269039 
Quantile  0.975 273039 
Mean            309730 
Stdev           2929.91 
Quantile  0.025 303562 
Quantile  0.25  308201 
Quantile  0.5   309703 
Quantile  0.75  311215 
Quantile  0.975 316034 
# Posterior mean and 95% CI
mn_data$PMoriginal <- sapply(marginals_summaries, '[[', "mean") 
mn_data$LLoriginal <- sapply(marginals_summaries, '[[', "quant0.025")
mn_data$ULoriginal <- sapply(marginals_summaries, '[[', "quant0.975")

# common legend
at <- seq(min(c(mn_data$PMoriginal, mn_data$LLoriginal, mn_data$ULoriginal)),
          max(c(mn_data$PMoriginal, mn_data$LLoriginal, mn_data$ULoriginal)),
          length.out = 8)

# popup table
popuptable <- leafpop::popupTable(dplyr::mutate_if(mn_data,
                                  is.numeric, round, digits = 2),
zcol = c("NAME", "vble", "HouseholdSizeE", "IncomeE", "PM", "LL", "UL"),
row.numbers = FALSE, feature.id = FALSE)

m1 <- mapview(mn_data, zcol = "PMoriginal",
              map.types = "CartoDB.Positron",
              at = at, popup = popuptable)
m2 <- mapview(mn_data, zcol = "LLoriginal",
              map.types = "CartoDB.Positron",
              at = at, popup = popuptable)
m3 <- mapview(mn_data, zcol = "ULoriginal",
              map.types = "CartoDB.Positron",
              at = at, popup = popuptable)
leafsync::sync(m1, m2, m3, ncol = 3)

Conclusion